Question

If the $nth$ term of an AP is $7-3n$ then find the sum of first twenty five terms.

Answer 1

Let first term of AP be, $a$

Common difference be $d$

According to question,

$nth$ term is => $7-3n=a+(n-1)d$

=> $a+nd-d=7-3n$

By comparing coefficents, we get

$a=4$ & $d=-3$

So, sum first $25$ terms,

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

=> $\frac{25}{2}[2\times 4+(25-1\left)\right(-3\left)\right]$

=> $\frac{25}{2}[8-72]$

=> $-400$