Question

Determine the sum of first 25 terms of an A.P whose second term is 7 and 27seventh
term is $157$

Answer 1

Let $a$ be the first term and $d$ be the common difference in an A.P

Given:$a+d=7$ ....$\left(1\right)$ and $a+26d=157$ ....$\left(2\right)$

Eqn$\left(2\right)-$Eqn$\left(1\right)=a+26d-a-d=157-7=150$

$\Rightarrow 25d=150$

$\Rightarrow d=\frac{150}{25}=6$

We have $a+d=7\Rightarrow a=7-d=7-6=1$

$\therefore S_{25}=\frac{25}{2}[2\times 1+(25-1)6]$

$=25[1+25\times 3]=25\times 76=1900$