Question

The first term of an A.P is $2$ and the last term is $50$. The sum of all these terms is $442$. Find the common difference.

Answer 1

Given:

$a=2,a_n=50$

$S_n=\frac{n}{2}[a+a_n]=442$

$a_n=a+(n-1)d\Rightarrow 50=2+(n-1)d\Rightarrow 48=(n-1)d$...(1)

$442=\frac{n}{2}[2+50]$

$n=2\times \frac{442}{2+50}=17$

From (1)

$48=(n-1)d$

$48=(17-1)d$

$\therefore d=3$