Question

The sum of first $15$ terms of an A.P. is $750$ and its first term is $15$. Find its ${20}^{th}$ term.

Answer 1

$S_n=\frac{n}{2}[2a+(n-1\left)d\right]$

$750=\frac{15}{2}\left[2\right(15)+(15-1\left)d\right]$

$100=30+14d$

$\therefore d=\frac{70}{14}=5$

$T_n=a+(n-1)d$

$T_{20}=15+(20-1)5$

$=15+95$

$\therefore T_{20}=110$