Question

Find the sum of the arithmetic series $5+11+17+....+95$.

Answer 1

Given series is $5+11+17+....+95$.

Thus, $a=5,d=11-5=6,l=95$
$n=\frac{l-a}{d}+1$
$=\frac{95-5}{6}+1$

$=\frac{90}{6}+1=15+1=16$
Therefore, $S_n=\frac{n}{2}(a+l)$

$=\frac{16}{2}(5+95)$

$=8\left(100\right)$

$=800$