Find the sum of the series : `5+13+21++181.`

Explanation

The terms of the given series form an A.P. with first term a=5 and common difference `d=13−5=21−13=8`

`a_n`` =181`

General term : `a_n` `=a+(n−1)d`

`a+(n−1)d=181`

`=>5+(n−1)×8=181`

`=>8n=184`

`=>n=23`

Therefore, required sum =`n/2(a+l)=23/2`(5+181)=2139.