Question

Find the sum to $n$ terms of the series
$5+11+19+29+......$

Answer 1

Given,

$5+11+19+29+......+n$

$11-5=6,19-11=8,29-19=10,.....$

Therefore the series reduces to,

$6+8+10+....+n$

Sum of this series is given by,

$S_n=2n+6$

when $n=0\to 2\left(0\right)+6=6$

when $n=1\to 2\left(1\right)+6=8$

when $n=2\to 2\left(2\right)+6=10$

when $n=n\to 2\left(n\right)+6=2n+6$