Question

The sum of successive odd numbers 1,3,5,7,9,11,13,15,17 is​

Answer 1

Given that,

A series 1,3,5,7,9,11,13,15,17.

To find,

The sum of successive odd numbers.

Solution,

The given sequence is in AP with,

First terms, a = 1

Common difference, d = 3-1 = 2

Number of terms, n = 9

The sum of nth term of an AP is given by :

$S_n=\dfrac{n}{2}[2a+(n-1)d]$

So,

$S_n=\dfrac{9}{2}[2\times 1+(9-1)\times 2]\\\\S_n=\dfrac{9}{2}\times (2+16)\\\\S_n=81$

So, the sum of successive odd numbers 1,3,5,7,9,11,13,15,17 is​ 81.