Question

If $S_1,S_2,S_3,....S_m$ are the sums of n terms of m A.P.'s whose first terms are 1,2,3,.....,m\) and common differences are $1,3,5,....2m-1$ respectively, then $S_1+S_2+S_3+....S_m=$

• A.
• B.
• C.
• D. None of the above

Answer 1

The correct option is A

Here $a=1,2,3,.....m;$ $d=1,3,5,....,2m-1$ and $n=n,$ then $S_1+S_2+.......+S_m=\frac{1}{2}mn(mn+1)$
$[\text{Using}S=\frac{m}{2}(a+l).\text{Since}{S}_1,S_2,S_3,...S_m\text{form an A.P.}]$