find the sum of the first 20 terms of an A.P.

The $n^{th}$ term of an arithmetic progression is given by $a_n=a_m+(n-m)(d)$ where $a_m$ is the $m^{th}$ term and $d$ is the common difference.

Computing for $d$ , we have

$25=-2+(20-2)(d)$ $\implies$ $d=1.5$

Computing for $a_1$ , we have

$a_1=-2+(1-2)(1.5)=-3.5$

The sum of the terms of an arithmetic progression is given by $s=\dfrac{n}{2}(a_1+a_n)$ where $n$ is the number of terms, $a_n$ is the $n^{th}$ term and $a_1$ is the first term. So we have

$s=\dfrac{20}{2}(-3.5+25) = 215$