x^2 - 27x + 182 = 0 | Solve by factorization method.

5x^2 - 6x - 2 = 0 | Solve by completing square.

Solve: 3^2x+1 = 9^2x-1

Solve: 2^x-4 = 4^x-6

4^2x-1 = 2^x+1

Solve: 3^x + 3^x+2 = 10/3

Solve: 2^x+3 + 2^x+1 = 80

Solve: 2^x+3 + 2^x = 36

Solve: 3^x+2 + 3^x+1 = 1 (⅓)

Solve: 2^x - 2^x-2 = 6

Solve: 2^y + 2^y-2 = 5

Solve: 2^x+1 - 2^x = 8

Solve: 3^x+1 - 3^x = 54

Solve: 2^x + 2^x+2 = 5

Solve: 3^x+3 + 1/(3^x) - 28 = 0

Solve: 2^x+3 + 1/(2^x) - 9 = 0

Solve: $\rm \frac{2^{x+1}}{16} + \frac{16}{2^{x+1}} = \frac{65}{8}$

Solve: $\rm 7^x + \frac{1}{7^x} = 49 \frac{1}{49}$

Solve: $\rm 2^x + \frac{1}{2^x} = 4 \frac{1}{4}$

Solve: $\rm 3^x + \frac{1}{3^x} = 9 \frac{1}{9}$

Solve: $\rm 3^{x-2} + 3^{3-x} = 4$

Solve: $\rm 5^{x-2} + 5^{3-x} = 6$

Solve: $\rm 3^{x-3} + 3^{4-x} = 4$

Solve: $\rm 2^{x-1} + 2^{-x} = 1 \frac{1}{2}$

Solve: $\rm 3^{x-3} + 3^{2-x} = 1 \frac{1}{3}$

Solve: $\rm 4^{x-4} + 4^{3-x} = 1 \frac{1}{4}$

Solve: $\rm 4^x - 6.2^{x+1} + 32 = 0$

Solve: $\rm 2^{2x+3} - 9.2^x + 1 = 0$

Solve: $\rm 3.9^x - 3^{x+1} + 1 = 3^x$

Solve: $\rm 5.4^{x+1} - 16^x = 64$

Solve: 4^x - 5.2^x + 4 = 0

Solve: 9^x = 4.3^x+1 - 27

Solve: 2^x + 2^x+1 + 2^x+2 + 2^x+3 + 2^x+4 = 62

Solve: 3^x + 3^x+1 + 3^x+2 + 3^x+4 = 846

Solve: 2^x-3 .2a^1-x = 2^3x-5.a^x-2

Solve: 2^4x+5.a^1-x = 4^x+32a^x-1

Prove that the values of x in the equation 3^x-2 + 3^3-x = 4 also satisfy the equation 4^x - 6.2^x+1 + 32 = 0.

Prove that the values of x in the equation 3^x-3 + 3^4-x = 4 also satisfy the equation 4^x-4 + 4^3-x = 1 (¼).

Prove that the values of x in the equation 5.4^x+1 + 16^x = 64 also satisfy the equation 9^x = 4.3^x+1 - 27.

Simplify: $\rm \frac{x^2}{y(x-y)} + \frac{y^2}{x(y-x)}$

Simplify: $\rm \frac{x^2}{y(x+y)} + \frac{y^2}{x(x+y)}$

Simplify: $\rm \frac{x^2 + y^2}{xy} - \frac{x^2}{y(x+y)} - \frac{y^2}{x(x+y)}$

Simplify: $\rm \frac{a^2 + b^2}{ab} - \frac{b^2}{a(a+b)} - \frac{a^2}{b(a+b)}$

Simplify: $\rm \frac{a-b}{a+b} - \frac{a+b}{a-b} + \frac{2ab}{a^2 - b^2}$

Simplify: $\rm \frac{a+b}{a-b} - \frac{a-b}{a+b} - \frac{2ab}{a^2-b^2}$

Simplify: $\rm \left ( 1 - \frac{1}{p} \right ) \left ( 1 -\frac{1}{p-1} \right ) \left ( 1 + \frac{2}{p-2} \right )$

Simplify: $\rm \left ( 1 - \frac{2}{m} \right ) \left ( 1 - \frac{1}{m-2} \right ) \left ( 1 - \frac{1}{m-3} \right ) $

Simplify: $\rm \frac{2}{(x-2)(x-3)} + \frac{2}{(x-1)(3-x)} + \frac{1}{(1-x)(2-x)}$

Simplify: $\rm \frac{1}{(x-3)(x+2)} + \frac{3}{(x+2)(4-x)} + \frac{2}{(x-3)(x-4)}$

Simplify: $\rm \frac{2(a-3)}{(a-4)(a-5)} + \frac{a-1}{(3-a)(a-4)} + \frac{a-2}{(5-a)(a-3)}$

Simplify: $\rm \frac{(a-b)^2 - c^2}{a^2 - (b+c)^2} + \frac{(b-c)^2 - a^2}{b^2 - (c+a)^2} + \frac{(c-a)^2 - b^2}{c^2 - (a+b)^2}$

Simplify: $\rm \frac{x+y}{x-y} - \frac{x-y}{x+y} + \frac{4xy}{x^2 + y^2}$

Simplify: $\rm \frac{2xy}{x^2 - y^2} - \frac{x-y}{x+y} + \frac{x+y}{x-y}$

Simplify: $\rm \frac{a+2}{1 + a + a^2} - \frac{a-2}{1 - a + a^2} - \frac{2a^2}{1 + a^2 + a^4}$

Simplify: $\rm \frac{y-2}{y^2 - 2y + 4} + \frac{y+2}{y^2 + 2y + 4} - \frac{16}{y^4 + 4y^2 + 16}$

Simplify: $\rm \frac{x+3}{x^2 + 3x + 9} + \frac{x-3}{x^2 - 3x + 9} - \frac{54}{x^4 + 9x^2 + 81}$

Simplify: $\rm \frac{2}{1 - a^2} + \frac{2}{1 + a^2} + \frac{4}{1 + a^4}$

Simplify: $\rm \frac{a+b}{2ab} \left ( a + b - c \right ) + \frac{b+c}{2bc} \left ( b + c - a \right ) + \frac{c+a}{2ca} \left ( c + a - b \right )$

Simplify: $\rm \left ( \frac{1}{a} + \frac{1}{b} \right ) \left ( a + b -c \right ) + \left ( \frac{1}{b} + \frac{1}{c} \right ) \left ( b + c -a \right ) + \left ( \frac{1}{c} + \frac{1}{a} \right ) \left ( c + a - b \right )$

Simplify: $\rm \frac{2}{(y+1)(y+2)} + \frac{1}{(y+1)^2 (y+2)^2} - \frac{1}{(y+1)^2}$

Simplify: $\rm \frac{1}{(x+1)^2 (x+2)^2} - \frac{1}{(x+1)^2} + \frac{2}{x+1} - \frac{2}{x+2}$

Simplify: $\rm \frac{2 (1 + c^4)}{1 - c^4} + \frac{4c^2}{1 + c^4} + \frac{8c^6}{1 - c^8}$

Simplify: $\rm \frac{1}{a+1} + \frac{2}{1 + a^2} + \frac{4}{a^4 - 1}$

Simplify: $\rm \frac{1}{a+b} + \frac{2a}{b^2 + a^2} + \frac{4a^3}{b^4 -a^4}$

Prove: $\rm \frac{2xy}{x^2 - y^2} + \frac{2xy}{x^2 + y^2} + \frac{4x^3y}{x^4 + y^4} = \frac{8x^7y}{x^8 - y^8}$

Prove: $\rm \frac{4x}{1 - x^2} + \frac{4x}{1 + x^2} + \frac{8x^3}{1 - x^4} = \frac{8x}{1-x^2}$

Prove: $\rm \frac{2}{a^2 - 1} - \frac{2}{a^2 + 1} - \frac{4}{a^4 + 1} = \frac{8}{a^8 - 1}$

Prove: $\rm \frac{2}{1 - x^2} - \frac{2}{1 + x^2} + \frac{4}{1-x^4} = \frac{4}{1-x^2}$

Prove: $\rm \frac{x - 3y}{x^2 - y^2} - \frac{3y}{y^2 - x^2} + \frac{xy}{x^3 + y^3} = \frac{x^3}{(x-y)(x^3 + y^3)}$

Prove: $\rm \frac{2x}{x^2 - 1} - \frac{2x}{x^2 + 1} - \frac{4x}{x^4 + 1} = \frac{8x}{x^8 - 1}$

Prove: $\rm \frac{3a-1}{a^2 - 1} + \frac{3a}{1 - a^2} + \frac{a}{1 + a^3} = \frac{1}{(1 - a)(1 + a^3)}$

Prove: $\rm \frac{a^3}{a-1} + \frac{a^3}{a + 1} - \frac{2}{1 - a^2} = 2(a^2 + 1)$

Find a: $\rm \frac{a}{x-y} - \frac{x+y}{x^2 - y^2} = 0$

Find a: $\rm \frac{a}{xy - y^2} + \frac{y}{xy - x^2} = \frac{x + y}{xy}$

Find a: $\rm \frac{1}{(x-y)(x-z)} - \frac{a}{(z-x)(y-z)} = \frac{1}{(x-y)(y-z)}$

Find b: $\rm \frac{b}{x-2} + \frac{x+3}{2-x} = \frac{1-x}{x-2}$

Find b: $\rm \frac{b}{x^2 - 5x} - \frac{x}{5x - 25} = - \frac{x + 5}{5x}$

Find a,b: $\rm \frac{a}{2x-3} - \frac{b}{3x + 4} = \frac{x + 7}{6x^2 -x-12}$

Find a,b: $\rm \frac{a}{x-5} - \frac{b}{x+3} = \frac{4(x+9)}{(x-5)(x+3)}$

Find a,b: $\rm \frac{a}{x+2} + \frac{b}{x} = \frac{8x + 10}{x(x+2)}$

Find the common difference and first term of an arithmetic series if the sum of the first 6 terms and 9 terms are 183 and 369 respectively.

If the sum of the first 10 terms of an arithmetic series is 27.5 and the 10th term of the series is 5, determine the value of its first term and common difference.

Find the arithmetic mean between $\rm \frac{15}{4}$and $\rm \frac{19}{4}$

Find the arithmetic mean between $\rm \frac{11}{2}$and $\rm \frac{15}{2}$

Find the arithmetic mean between $\rm \frac{2}{9}$and $\rm \frac{6}{7}$

Find the arithmetic mean between $\rm (a + b) $ and $\rm (a - b )$

Find the arithmetic mean between $(\rm \frac{p}{2} + \frac{q}{2} )$and $(\rm \frac{q}{2} - \frac {p}{2})$

Find the arithmetic mean between $\rm 6x^{2} $ and $\rm 2x^{2}$

If the arithmetic mean between two numbers is 20 and the first number is 28, find the second number.

If the arithmetic mean between two numbers is 40 and the first number is 35, find the second number.

Insert 5 arithmetic means between -7 and 17.

Insert 6 arithmetic means between -3 and 32.

Insert 3 arithmetic means between 2 and 10.

Insert 4 arithmetic means between 1 and 16.

If 13, p, q, r, 29 are in arithmetic sequence, find the values of p, q, and r.

Find the values of p, q, and r, if 15, p, q, r, 35 are in arithmetic sequence.

If 8, x, y, z, -4 are in an arithmetic sequence, find the values of x, y, and z.

If 3, p, q, r, and 9 are in arithmetic sequence, find the values of p, q, and r.

There are n arithmetic means between 12 and 33. If the fourth mean is 24, 

1. Find the value of common difference.
2. Find the value of n.

There are k arithmetic means between 15 and 45. If the third mean is 30,

1. Find the value of common difference.
2. Find the value of k.

There are 'n' arithmetic means between 2 and 11 where the ratio of the first mean is to the last mean is 7: 19.

1. Find the common difference in terms of n.
2. Find the value of n.

There are n arithmetic mean between 5 and 35 such that the second mean: last mean is 1:4.

1. Find the common difference in terms of n.
2. Find the value of n.

There are 6 arithmetic means between a and b. If the second mean and last mean are 8 and 20 respectively.

1. Find the value of a.
2. Find the value of b.

3 arithmetic means are inserted between a and b. If the first and third means are 16 and 34 respectively,

1. Find the value of a.
2. Find the value of b.

28 arithmetic means are inserted between a and b so that the two means exactly in the middle are 59 and 63.

1. Find the value of a.
2. Find the value of b.

10 arithmetic means are inserted between a and b so that the two means exactly in the middle are 11 and 13.

1. Find the value of a.
2. Find the value of b.

Divide 6 into three parts, which are in arithmetic sequence, such that their product is-24

The product of two numbers is 375 and their arithmetic mean is 20. Find the numbers.

Divide 24 into three parts, which are in arithmetic sequence, such that their product is 224.

In a flower bed there are 23 rose plants in the first row, 21 in the second row and 19 in the third row and so on. There are 5 plants in the last row.

1. Is this sequence are in arithmetic progression?
2. How many flower beds are there? 
3. How many plants are there in $\rm 6^{th}$ row? 
4. Find the arithmetic means between 23 and 5.

Sharmila started to work in 2075 BS at an annual salary of Rs 2,50,000 and received a Rs 10,000 rise every year. 

1. Which sequence is related to given situation?
2. In what year would her annual salary reach Rs 3,50,000?
3. Find the monthly salary of Sharmila on $\rm 8^{th}$ years.
4. Fnd the means between 2,50,000 and Rs 3,00,000..

Find the sum of the series $\rm 5 + 11 + 17 + \dots $ to 20 terms.

Find the sum of the series $\rm 12+9+6+\dots$ to $32$ terms

Find the sum of the series : $\rm - 3 + 1 + 5 + \dots $ to $\rm 50$ terms.

Find the sum of the series: $\rm 1+\frac{1}{4}-\frac{2}{4}-\frac{5}{4} - \dots $to $10$ terms.

Calculate the sum of the series of natural numbers: $\rm 1 + 2 + 3 + 4 + \dots $ to $20$ terms.

Calculate the sum of the series of natural numbers: $\rm 1 + 2 + 3 + 4 + \dots $ to $15$ terms.

Calculate the sum of the series of natural numbers: $\rm 1 + 3 + 5 + 7 + \dots $ to $20$ terms.

Calculate the sum of the series of natural numbers: $\rm 1 + 3 + 5 + 7 + \dots $ to $30$ terms.

Calculate the sum of the series of natural numbers: $\rm 2 + 4 + 6 + 8 + \dots $ to $25$ terms.

Calculate the sum of the series of natural numbers: $\rm 2 + 4 + 6 + 8 + \dots $ to $40$ terms.

Find the sum of n terms of the series: $\rm 5 + 8 + 11 + 14 + 17 +\dots $

Find the sum of n terms of the series: $\rm 3 + 5 + 7 + 9 + 11 + \dots $

Find the sum of n terms of the series: $\rm \frac{1}{2} + 1 + \frac{3}{2} + 2 +\frac{5}{2} + 3 + \dots $

Find the sum of n terms of the series: $\rm \frac {1}{4} +\frac {1}{2} + \frac {3}{4} + 1  + \frac {5}{4} + \frac {3}{2} + \dots $

Calculate the sum of 20 terms of the series whose $\rm n^{th}$ terms is: $\rm 4n - 3$.

Calculate the sum of 20 terms of the series whose $\rm n^{th}$ terms is: $\rm n - 3$.

Calculate the sum of 20 terms of the series whose $\rm n^{th}$ terms is: $\rm 2n + 1$.

Calculate the sum of 20 terms of the series whose $\rm n^{th}$ terms is: $\rm 8 - n$.

Find the sum of the series: $ \sum_{n=1}^{11}(n+7) $.

Find the sum of the series: $\rm \sum_{n=3}^{10}(n+ 6) $.

Find the sum of the series: $\rm \sum_{n=4}^{12}(3n + 2) $.

Find the sum of the series: $\rm \sum_{n=4}^{12}(5n - 4) $.

Find the sum of the series: $\rm 9 + 11 + 13 + \dots + 99$.

Find the sum of the series: $\rm 7 + 10 + 13 + 16+ \dots + 67$.

Find the sum of the series: $\rm - 15 - 5 + 5 + \dots + 115$

Find the sum of the series: $\rm - 8 - 6 - 4 - 2 + 0 + 2 + \dots + 40$.

Find the common difference and first term of an arithmetic series if the sum of the first 6 terms and 9 terms are 183 and 369 respectively.

If the sum of the first 10 terms of an arithmetic series is 27.5 and the $\rm 10^{th}$ term of the series is 5, determine the value of its first term and common difference.

If the first term (a = 3), the last term (b = 90), and the sum is 1395, then find the number of terms and common difference.

If the first term (a = 79), the last term (b = 7), and the sum is 1118, then find the number of terms and common difference.

If the first term (a = 9), the last term (b = -6), and the sum is 24, then find the number of terms and common difference.

If the first term (a = 1), the last term (b = $\rm 58 \frac {1}{2}$), and the sum is 714, then find the number of terms and common difference.

The sum of three numbers in an A.S. is 39 and their product is 2184. Find the numbers

Three numbers are in AS. If the sum of these numbers is 27 and the product is 585, find the numbers.

The sum of five numbers in an A.S. is 15 and the sum of their squares is 55. Find the numbers.

How many terms of the series $\rm 24 + 20 + 16 +\dots $ must be taken so that the sum may be 72?

How many terms are there in A.S. Whose first term and fifth term are -14 and 2 respectively, and the sum of the terms is 40?

How many terms of the series $\rm 42 + 39 + 36 + \dots $ make the sum 315? Explain the double answer.

How many terms must be taken of the series$\rm - 16 - 15 - 14 - \dots $ makes the sum -100? Explain the double answer.

If the third term of an A.S. is 7 and $\rm 7^{th} $ terms exceeds 3 times the third term by 2, find the sum of first 30 terms.

The sum of $\rm 4^{th}$ and $\rm 8^{th}$ terms of an A.S. is 70, and the sum of $\rm 6^{th}$ and $\rm 10^{th}$ term is 94. Find sum of first 20 terms.

If $\rm 9^{th}$ and $\rm 20^{th}$ terms of an A.S. are 18 and 40 respectively, find the sum of the first 29 terms.

If the $\rm 6^{th}$ term of an A.S. is 64, find the sum of the first 11 terms.

If the $\rm 7^{th}$ term of an A.S. is 70, find the sum of the first 13 terms.

Find the sum of the first 29 terms of an AS if its $\rm 15^{th}$ term is 2.

In an Arithmetic sequence, the sixth term is equal to three times the fourth term and the sum of the first three terms is -12. Find the sum of the first ten terms.

Fourteenth term of an arithmetic series is 2 and the sum of its first ten terms is -150. Find the sum of the first twenty-five terms of the series.

The sum of the first 9 terms of an arithmetic series is 72 and the sum of the first 17 terms is 289. Find the sum of the first 25 terms.

The sum of the first 7 terms of an arithmetic series is 14 and the sum of the first 11 terms is 66. Find the sum of the first 25 terms.

The first and last terms of an arithmetic series are -24 and 72 respectively. If the sum of all terms of the series is 600, find the number of terms and the common difference of the series.

In an AS, the sum of the first ten terms is 520. If its seventh term is double of its third term calculate the first term and the common difference of the series.

The sum of first 9 terms of an arithmetic series is 90 and the ratio of the third term and sixth term is 1 : 2. Find the first term and $\rm 8^{th}$ term. 

The sum of the first 6 terms of an arithmetic series is 63 and the ratio of the second term and fifth term is 2 : 5. Find the first term and $\rm 10^{th}$ term.

If the first 3 terms of an arithmetic series are p+2, 2p-1, and p+6 respectively, find p and the sum of its first five terms. 

2(k-1), k+2 and 3k are the three terms of an AP. Find the value of k and the sum of the first 5 terms

There are 125 passengers in the first carriage, 150 passengers in the second carriage and 75 passengers in the third carriage, and so on in an arithmetic sequence. What's the total number of passengers in the first 7 carriages?

A car travels 300 m in the first minute, 420 m in the next minute, 540 m in the third minute, and so on in an arithmetic sequence. What's the total distance the car travels in I hour?

A writer wrote 890 words on the first day, 760 words on the second day and 630 words on the third day, and so on in an arithmetic sequence. How many words did the writer write in a week?

20 people live on the first floor of a building, 34 people on the second floor and 48 people on the third floor, and so on in an arithmetic sequence. There is a 5 storeyed building. What's the total number of people living in the building? Find by using the formula.

Kuber saves Rs 100 during the first month, Rs 150 in the next month, and Rs.200 in the third month. If he continues his saving in this sequence,

1. In how many months will he save Rs 257500?
2. Find the total savings at the end of 7 years. 
3. What will be the amount of savings only in the $\rm 20^{th}$ month? 

Ashma saves Rs 111 during the first month, Rs 222 in the next month, and Rs 333 in the third month. If she continues saving in sequence,

1. In how many months will she save Rs 560550?
2. Find the total savings at the end of 5 years.
3. What will be the amount of savings only in $\rm 22^{nd}$ month?

Mithailal repays a loan of Rs 29000 on installment based system by paying certain amount in the first month and then increases the installment by Rs 100 every month so that it takes 20 months to clear the loan. Find the amount of the first installment.

Ramjanam repays a loan of Rs 189000 on installment based system by paying certain amount in the first month and then increases the installment by Rs 400 every month so that it takes 30 months to clear the loan. Find the amount of first installment.

Abdul repays a loan of Rs 193750 by paying Rs 200 in the first month and then increases the payment by Rs 150 every month. How long will it take him to clear the loan?

Sonika repays a loan of Rs 632500 by paying Rs 400 in the first month and then increases the payment by Rs 500 every month. How long will it take her to clear the loan?

A class consists of a number of boys whose ages are in AP. The common difference is 4 months. If the youngest boy of the class be only 8 years and the sum of the ages of all boys be 168 years, find the number of boys and age of the oldest boy.

A community consists of a number of people whose ages are in AP. The common difference of their ages is 3 months. The youngest people is of 10 years and the sum of their ages is 341 years 3 months. Find the total number of people and the age of eldest people.

A cricket team consists of a number of players whose ages are in AP. The common difference of their ages is 4 months. The youngest player is of 18 years and the sum of their ages is 550 years. Find the total number of players and the age of the eldest player.

A brick staircase has a total of 40 steps. The bottom step requires 500 bricks. Each successive step requires 10 less bricks than the prior step.

1. How many bricks are required for the top step?
2. How many bricks are required to build the staircase?

A stadium has 50 rows. The first row has 40 seats and each successive row has 8 additional seats.

1. How many seats are there in the last row? 
2. How many seats are there in the stadium in total?

Find the geometric mean between: 3 and 12.

Find the geometric mean between: 256 and 64.

Find the geometric mean between: 25 and 625.

Find the geometric mean between: -4 and -25.

Find the geometric mean between: 8 and $\frac{32}{3}$.

Find the geometric mean between: $\frac{1}{64}$ and $\frac{1}{16}$.

Find the $\rm 2^{nd}$ term of a geometric sequence whose first and third terms are $\rm \frac{2}{3}$ and$\rm \frac{3}{2}$ respectively.

If the geometric mean between two numbers is 27 and the first number is 81, find the second number.

Two numbers are in the ratio of 2 : 1 and their geometric mean is 4. Find the numbers.

Two numbers are in the ratio of 8 : 3 and their geometric mean is $\rm\frac{1}{4}$, Find the numbers.

Insert 3 geometric means between 6 and 96.

Insert 3 geometric means between 5 and 80.

Insert 4 geometric means between 2 and 64.

Insert 4 geometric means between 1 and 243.

Insert 5 geometric means between 8 and $\rm \frac{1}{8}$.

1f 6, x, y, 162 are in a geometric sequence, find the values of x and y.

-16, x, y, 54 are in a geometric sequence, find the values of x and y.

If 5, x, y, z, and 405 are in a geometric sequence, find the values of x, y, and z.

If $\rm \frac{1}{81}$, p, q, m, and 1 are in a geometric sequence, find the values of p, q, and m.

There are some geometric means between 3 and 192 in such a way that the $\rm 5^{th}$ geometrical mean is 96. Find the number of means.

How many geometric means are there between 10 and 1280, where the ratio of the first mean is to the last mean is as 1 : 32?

There are 5 geometric means between a and b. If the second mean and last mean are 63 and 1701 respectively, find the values of a and b. 

4 geometric means are inserted between a and b. If the first and third means are 54 and 24 respectively, find the values of a and b.

The arithmetic mean of two numbers is 15 and their geometric mean is 9. Find the numbers.

The AM of two numbers is 34 and their GM is 16. Find the numbers.

The AM of two numbers is 25 and their GM is 20. Find the numbers.

p+9, p-6, and 4 are the first three terms of a geometric sequence. Find the $\rm 5^{th}$ term.

3x, x+6, and 3x+8 are the first three terms of a geometric sequence. Find the $\rm 4^{th}$ term.

2k, 2k+3, and 2k+9 are the first three terms of a geometric sequence. Find the $\rm 6^{th}$ term.

Find the two numbers whose AM and GM are given below: Also, verify the result using relations greater number = $\rm AM + \sqrt {AM^2 - GM^2}$ and smaller number = $\rm AM - \sqrt {AM^2 - GM^2}$

1. AM = 25 and GM = 24
2. AM = 29 and GM= 2I
3. AM = 41 and GM = 40
4. AM = 37 and GM = 35

In a shop, 5 pens are sold on the first day and the double number of pens are sold in everyday as comparison of previous day.

1. Which progression is associated with this situation?
2. On which day does he sell 160 pens?
3. How many pens does he sell in $\rm 9^{th}$ day?

Jenisha borrows Rs 4368 which she promises to pay in 6 annual installments, each installment being treble of the preceding one.

1. Which progression is associated with given situation?
2. Find the amount of the first installment.
3. Find the amount of the last installment.

Find the sum of the geometric sequence: $\rm 1, 2, 4, \dots $, to 10 terms.

Find the sum of the geometric sequence: $\rm 128, 64, 32, \dots $, to 15 terms.

Find the sum of the geometric sequence: $\rm 1, -3, 9, -27, \dots $, to 9 terms.

Find the sum of the geometric sequence: $\rm 1, -2, 4, \dots $, to 11 terms.

Find the sum of the geometric sequence: $\rm 32, 48, 72, \dots $, to 8 terms.

Find the sum of the geometric sequence: $\rm 2, -16, 18, -54, \dots $, to 6 terms.

Find the sum of the geometric series whose first term is 1, the common ratio is 3, and the last term is 243.

Find the sum of the sequence, $\rm 2^1, 2^2, 2^3, 2^4, \dots ,$ to 10 terms.

Find the sum of the sequence, $\rm 3^6, 3^5, 3^4, \dots ,$ to 15 terms.

Find the number of terms and the common ratios of a geometric series when the first term is 7, the last term 189, and the sum 280.

Find the number of terms and the common ratios of a geometric series when the first term is 2, the last term 486, and the sum 728.

Find the number of terms and the common ratios of a geometric series when the first term is 5, the last term is 320, and the sum is 635.

Find the number of terms and the common ratios of a geometric series when the first term is 3, the last term is 384 and the sum is 765.

Find the sum of the geometric series: $\rm \sum_{n = 3}^{5}3(4)^{n-2}$.

Find the sum of the geometric series: $\rm \sum_{n = 3}^{8}2(-2)^{n}$.

Find the sum of the geometric series: $\rm \sum_{n = 1}^{5} (3)^{n + 1}$.

Find the sum of the geometric series: $\rm \sum_{n = 4}^{12}2(5)^{n - 4}$.

How many terms must be taken of: the series $\rm 32 + 48 + 72 + \dots $ to make the sum 665?

How many terms must be taken of: the series $\rm 4 + 8 + 16 +\dots $ to make the sum 508?

How many terms must be taken of: the series $\rm 64 + 96 + 144 + \dots $, to make the sum 1330?

How many terms must be taken of: the series $3 + 6+12 + \dots $ to make the sum 1533?

How many terms must be taken of: the series $\rm 9 + 3 + 1 + \dots $to make the sum $\rm \frac{121}{9}$?

If the first term of a positive geometric series is 3 and 3$^{rd}$ term is 12, find the sum of its first 8 terms.

The 2$^{nd}$ and 5$^{th}$ terms of a geometric series are 3 and 81 respectively. Find the sum of its first 7 terms.

The sum of the first 3 terms of a GS is 292 and its common ratio is 8. Find the first term of the series.

The common ratio of a geometric series is 3 and the sum of its first 4 terms is 80. Find the first term.

The sum of 1$^{st}$ 6 terms of a GP is 28 and sum of first 3 terms is 1. Find its common ratio and first term.

The sum of the first two terms and four terms of a GP are 3 and 15 respectively. Find the sum of its first six terms, if the common ratio is positive.

The sum of three numbers in a geometric series is 31 and their product is 125. Find the numbers.

The product of three numbers in a GS is 27 and the sum of their products in pairs is 39. Find the numbers.

Three numbers are in a geometrical series and their sum is 15. If 1, 3, and 9 are added to them respectively, they form a geometric series, find the numbers.

Three numbers are in a geometric series and their product is 1000. If 6 and 7 are added to the second and third terms respectively, they form an arithmetic series, find the numbers.

Three numbers are in an arithmetic series and their sum is 18. If the first two numbers are increased by 4 each and the third is increased by 36, they form a geometric series. Find the numbers.

The sum of the first 6 terms of a GS is 9 times the sum of the first 3 terms. Find the common ratio.

The sum of the first three terms and the sum of the first six terms of a geometric series are in the ratio 125: 152. Find the common ratio.

There are 8 varieties of monkeys in a zoo. The number of each variety forms a GP. If the $\rm 4^{th}$ and $\rm 6^{th}$ variety consist of 54 and 486 monkeys respectively,

1. Find the number in the first variety.
2. Find the number in the last variety.
3. Find the total number of monkeys in zoo.

There are 10 varieties of birds in a zoo. The number of birds in each variety being double of the number of another variety. If the number in the first variety is 2,

1. Find the number in the fifth variety.
2. Find the number in the last variety.
3. Find the total number of birds in the zoo.

There are 8 baskets full of flowers. The numbers of flowers in each basket form a GP. If the 4$^{th}$ and 6$^{th}$ baskets contain 24 and 96 flowers respectively,

1. Find the number of flowers in the first basket. 
2. Find the number of flowers in the last basket.
3. Find the total number of flowers.

The present ages of the elder and younger brothers are 13 years and 7 years respectively.

1. Find the ages of two brothers after x years in terms of x.
2. If the product of their ages after x years will be 280, find the value of x.
3. Find their ages after 10 years. 
4. Find their ages before 5 years.

The present ages of a father and his son are 35 years and 12 years respectively.

1. Find the ages of father and son before x years in terms of x.
2. If the product of their ages before x years was 210, find the value of x.
3. Find their ages after 15 years.
4. Find their ages before 10 years. 
    

The difference of the present ages of two brothers is 4 years.

1. If the present age of younger brother be x years then find the ages of elder brother in terms of x.
2. Find their ages before 5 years in terms of x.
3. If the product of their ages before 5 years was 96 then find the value of x.
4. Find their ages after 5 years.

The difference of the present ages of two sisters is 5 years.

1. If the present age of younger sister be x years then, find the ages of elder sister in terms of.x.
2. Find their ages after 4 years in terms of x.
3. If the product of their ages becomes 104, find the value of x.
4. Find their ages before 2 years.

The difference of the present ages of two brothers is 4 years and the product of their ages is 221. 

1. If x and y be the ages of two brothers then write the equation to represent given equations.
2. Find the value of x.
3.  Find the value of y.
4. Find their ages after 5 years.

The difference of the present ages of two sisters is 5 years and the product of their ages is 204.

1. If the age of the younger sister be x years then write the age of the elder sister in terms of x.
2. Find the value of x.
3. Find the present age of the elder sister.
4. Find their ages after 5 years.

The difference of the present ages of two sisters is 5 years and the product of their ages is 84.

1. If the age of the younger sister be x years then write the age of elder sister in terms of x.
2. Find the value of x. 
3. Find the present age of the elder sister. 
4. Find their ages after 10 years.

The difference of the present ages of two brothers is 7 years and the product of their ages is 44.

1. If the age of the younger brother be m years then write the age of the elder brother in terms of m.
2. Find the value of m.
3. Find the present age of the elder brother.
4. Find their ages before 3 years.

The sum of the present ages of elder and younger brothers is 30 years and the product of their ages is 221.

1. If the present age of the younger be 'a' years then find the ages of the elder brother in terms of a.
2. Find the value of a.
3. Find the present age of the elder brother.
4. What will be the product of their ages after 5 years?

The sum of the present ages of elder and younger sisters is 28 years and the product of their ages is 187.

1. If the present age of the younger sister is n years then find the present age of the elder sister in terms of n.
2. Find the value of n.
3. Find the present age of the elder sister.
4. What will be the product of their ages after 4 years?

The product of the present ages of two sisters is 150. 5 years ago, the elder sister was twice as old as her younger sister.

1. If the age of the younger sister before 5 years be p years then find that of the elder sister in terms of p.
2. Find their present ages in terms of p.
3. Find the value of p.
4. Find the present ages of two sisters.

The product of the present ages of two brothers is 160. 4 years ago, the elder brother was two years as old as his younger brother.

1. If the age of the younger brother 4 years ago was 'w' years then write the age of the elder brother 4 years ago.
2. Write the present ages of two brothers in terms of w.
3. Find the value of w.
4. Find their present ages, 
    

6 years ago, a man's age was 6 times the age of his son. The product of the present ages of the father and his son is 396.

1. If the age of the son 6 years ago be ‘y’ years then write the age of the father before 6 years in terms of y.
2. Write the present ages of the man and his son in terms of y.
3. What is the value of y?
4. Find their present ages.

One year hence, a father's age will be 5 times as old as his son's age. The product of the present ages of the father and his son is 145.

1. If the age of the son one years hence be ‘x’ years then write the age of the father one year hence in terms of ’x'.
2. Write their present ages in terms of x.
3. Find the value of x.
4. Find their present ages. 
    

The sum of two numbers is 21 and the sum of their squares is 261.

1. If one number be x then find other number in terms of x.
2. Write an equation to represent "sum of their squares is 261".
3. Find the value of x.
4. What is the difference of their squares?

The sum of the numbers is 16 and the sum of their squares is 130.

1. If one number be x then find other number in terms of x.
2. Write an equation to represent "sum of their squares is 130"
3. Find the value of x.
4. What is the difference of their squares?

In a two-digit number, the product of the digits is 18 and their sum is 9.

1. If the digit in unit place be 'u' then write the digit in tenth place in terms of u.
2. If the product of the digits be 18 then find the value of ‘u’.
3. Find the two-digit number.
4. By what percent this will be changed when the digits are reversed?

The sum of digits of a two-digit number is 7 and their product is 12.

1. If the digit in unit place be 'x' then write digit in tenth place in terms of x.
2. If the product of the digits be 12 then find the value of ‘x’.
3. Find the two-digit number.
4. By what percent this will be changed when the digits are reversed? 

The product of digits in a two-digit number is 12. The number formed by interchanging the digits of that number will be 9 less than the original number.

1. If y and x be the digits at unit place and tens place then write the two-digit number.
2. Write the number formed by interchanging the digits in terms of x and y.
3. Form the equations to represent given statements.
4. Find the values of x.
5. Find the two-digit numbers.

In a two-digit number, the product of two digits is 14 and if 45 is subtracted from the number, the number will be reversed.

1. If b and a be the digits at unit place and tens place then write the two-digit number.
2. Write the number formed by interchanging the digits in terms of a and b.
3. Form the equations to represent given statements.
4. Find the values of a.
5. Find the two digits numbers.

The sides of a right-angled triangle containing the right angle are less than its hypotenuse by 5 cm and 10 cm respectively.

1. If the hypotenuse of the triangle be 'h' then write other sides in terms of h. 
2. Find the value of h.
3. Find the sides of the right-angled triangle.

The sides of a right-angled triangle containing the right angle are less than its hypotenuse by 1 em and 8 cm respectively.

1. If the hypotenuse of the triangle be 'h' then write other sides in terms of h.
2. Find the value of h.
3. Find the sides of the right-angled triangle.

In an equilateral triangle, the size of the arm is x cm. All three sides of the triangle should be reduced by 12 cm, 13 cm, and 14 cm respectively to form a new right-angled triangle. Based on that, answer the following questions.

1. Draw a right-angled triangle after the reduction of sides by the given measure and label the sides in terms of x.
2. Find the value of x.
3. What is the size of the side of the equilateral triangle, write the reason.

In an equilateral triangle, the size of the arm is x cm. All three sides of the triangle should be reduced by 2 cm, 4 cm, and 6 cm respectively to form a new right-angled triangle. Based on that, answer the following questions.

1. Draw a right-angled triangle after the reduction of sides by given measure and label the sides in terms of x.
2. Find the value of x.
3. What is the size of the side of the equilateral triangle shown, write the reason.

Rs 4500 was distributed equally among a certain number of people. If there were 25 people more, each would have received Rs 9 less.

1. Among how many people was the amount distributed?
2. Find the share of each person.

A card is drawn from a pack of playing cards and a dice is thrown. Events A and B are as follows: 

A: 'Jack is drawn from the pack' & B: ‘ a one is thrown on the dice’.

1. Write down the values of P(A), P(B)
2. Write down the value of P(A and B).

There are 3 geometric means between 3 and 243.

1. First term 'a', last term 'b', and the number of geometric means 'n' are given. Write the formula for the calculation of the common ratio in the given condition.
2. What is the third mean of the given series? Find it.
3. In arithmetic mean and geometric mean between 3 and 243, which one is greater and by how much? Compare it.