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

(a) 2139
(b) 2476
(c) 2219
(d) 2337

Anurag Mishra Professor Asked on 4th May 2016 in Maths.
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1 Answer(s)

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. 

Anurag Mishra Professor Answered on 4th May 2016.
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