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. $\frac{1}{2}mn(mn+1)$
• B. $mn(m+1)$
• C. $\frac{1}{4}mn(mn-1)$
• D. None of the above

Answer 1

The correct option is A $\frac{1}{2}mn(mn+1)$

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