Given : The series 5+13+21+…+181.
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=n/2[a+l]
Substitute the values,
S_{23}=23/2[5+181]
S_{23}=23/2 x 186
S_{23}=23 x 93
S_{23}=2139
Therefore, The sum of the series 5+13+21+…+181 is 2139