# The sum of the series 5+13+21+…….+181 is:

(a) 2139

(b) 2476

(c) 2219

(d) 2337

**Answer: (a) 2139 **

**Solution:-**

The given series –

5 + 13 + 21 + …… + 181.

It is an arithmetic series.

First term (a) = 5

Common difference (d) = 13 – 5 = 8.

Let 181 be nth term of the given series. **Formula – ****nth term = a + (n – 1) d**

Therefore,

181 = 5 + (n – 1) x 8

181 = 5 + 8 n – 8

181 = 8 n – 3

8 n = 181 + 3

8 n = 184

n = 184/8

n = 23

**Formula- Sum of n term (S) n = n (a + l)/2 **

**Where, l = last term of the series.**

Then, sum of 23 term = 23 (5 + 181)/2

= 23 x 186/2

= 23 x 93

= 2139

Then, the sum of the series is 2139.

Hence, the correct answer is option (a) 2139.