CBSE Class 10 Maths (Standard) 2016 · Paper 30/3 · Question 20

The sums of first $n$ terms of three arithmetic progressions are $S_1$, $S_2$ and $S_3$ respectively. The first term of each A.P. is $1$ and their common differences are $1$, $2$ and $3$ respectively. Prove that $S_1+S_3=2S_2$.