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.

The sum of first n odd natural numbers is

Let A be the arithmetic mean and G be the geometric mean between two numbers a and b, then which of the following inequality holds?

How many terms must be taken of the series 3+6+12+..., to make the sum 1533?