In an AP it is given that Sn = qn2 and Sm = qm2. Prove that Sq = q3.

Q3 of 102 Page 429

In an AP it is given that S_n = qn² and S_m = qm². Prove that S_q = q³.

Given: S_n = qn² , S_m = qm²

To prove: S_q = q³

Put n = 1 we get

a = q …… equation 1

Put n = 2

2a + d = 4q ……equation 2

Using equation 1 and 2 we get

d = 2q

S_q = q³

Hence proved.

If the sum of n terms of an AP is given by S_n = (2n² + 3n), then find its common difference.

If 9 times the 9^th term of an AP is equal to 13 times the 13^th term, show that its 22^nd term is 0.

Find three arithmetic means between 6 and - 6.

The 9^th term of an AP is 0. Prove that its 29^th term is double the 19^th term.