Answer
$-70$
Work Step by Step
$a_{n+1}-a_n=\frac{2}{5}(n+1)-8-\left(\frac{2}{5}n-8\right)=\frac{2}{5}$
Since the difference between consecutive terms is constant, the given sequence is arithmetic.
The formula for the finite sum of the arithmetic sequence is:
$S_{n}=\frac{n(a_{1}+a_{n})}{2}$
$a_{n}=\frac{2}{5}n-8$
$a_{1}=\frac{2}{5}(1)-8=-\frac{38}{5}$
.
$a_{25}=\frac{2}{5}(25)-8=2$
$S_{25}=\frac{25(a_{1}+a_{25})}{2}=\frac{25\left(-\frac{38}{5}+2\right)}{2}=-70$
