Question

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

Answer 1

thus the sum of the given AP is 2139

Answer 2

Answer:

The sum of the series 5+13+21+...+181 is 2139.  

Step-by-step explanation:

Given : The series 5+13+21+...+181.

To find : The sum of the series?

Solution :

The given series 5+13+21+...+181 is in Arithmetic progression as there difference is same.

The first term in A.P is a=5

The common difference in the AP is d=13-5=21-13=8.

The last term is l=181.

The last term formula is,

$l=a+(n-1)d$

$181=5+(n-1)8$

$176=(n-1)8$

$n-1=22$

$n=23$

Now, The sum of the A.P series is

$S_n=\frac{n}{2}[a+l]$

Substitute the values,

$S_{23}=\frac{23}{2}[5+181]$

$S_{23}=\frac{23}{2}\times 186$

$S_{23}=23\times 93$

$S_{23}=2139$

Therefore, The sum of the series 5+13+21+...+181 is 2139.