Answer
$1575$
Work Step by Step
$a_{n+1}-a_n=6(n+1)-15-(6n-15)=6$
As the difference between consecutive terms is constant, the given sequence is arithmetic.
The formula for the finite sum of the arithmetic sequence is:
$S_{n}=\frac{n(a_{1}+a_{n})}{2}$
$a_{n}=6n-15$
$a_{1}=6(1)-15=-9$
.
$a_{25}=6(25)-15=135$
$S_{25}=\frac{25(a_{1}+a_{25})}{2}=\frac{25(-9+135)}{2}=1575$
