Question

The $7^{th}$ term of an AP is $32$ and its ${13}^{th}$ term is $62$ find first $5$ terms of the AP.

Answer 1

$7^{th}$ term $\Rightarrow a+6d=32$ ……….$\left(1\right)$ $[n^{th}terms=a(n-1\left)d\right]$

${13}^{th}$ term $\Rightarrow a=12d=62$

$\therefore -6d=-30$

$d=5,$ [Put in $\left(1\right)$]

$a+6\left(5\right)=32$

$\Rightarrow a=2$

Sum of five terms $=\frac{n}{2}(2a+(n-1\left)d\right)$

$=\frac{5}{2}(2\times 2+(5-1\left)5\right)$

$=\frac{5}{2}(4+20)$

$=60$.