Question

Find the sum to n terms of the series
$05+11+19+29+$......?

Answer 1

Given,

$05+11+19+29+...+n$ terms

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

Therefore the given series reduces to:

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

$S_n=2n+6$

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