Question

OR
The sum of first n terms of three arithmetic progressions are S, S and Sz respectively. The first termd
each A.P. is 1 and common differences are 1, 2 and 3 respectively. Prove that S,+ S3 - 2s2​

Answer 1

Answer:

$S1 + S3 = \frac{n}{2} (n + 1) + \frac{n}{2} (3n - 1) \\ = \frac{n}{2} (n + 1 + 3n - 1) \\ = \frac{n}{2} (4n) \\ = 2 {n}^{2} \\ = 2S2$

Hence proved