Question

If there be m A.P.'s beginning with unity whose common differences are $1,2,3,$_______m respectively, then the sum of their nth terms is $\frac{1}{2}m[mn-m+n+1]$.

• A. True
• B. False

Answer 1

The correct option is A True

Here the number of terms for all nth terms of $m$ AP series is $=m$

First term of the series $\Rightarrow$ $a=n$

The common difference of the series

$d=(2n-1)-n=n-1$

So applying formula

$S=\frac{m}{2}(2n+(m-1\left)\right(n-1\left)\right)$

$S=\frac{m}{2}(2n+mn-m-n+1)$

$S=\frac{m}{2}(mn-m+n+1)$

Hence, this is the answer.