Q. 244.0( 5 Votes )

(5 + 13 + 21 + + 181) =?
A. 2476

B. 2337

C. 2219

D. 2139

Answer :

Here, first term = 5


Common difference = d = 13 - 5 = 8


Last term = l = 253


To find: number of terms in the Arithmetic series


So, nth term is given by:


an = a + (n - 1)d


181 = 5 + (n - 1) × 8


181 - 5 = 8n - 8


176 = 8n - 8


176 + 8 = 8n


8n = 184


n = 23


Thus there are 23 terms in the arithmetic series.


Sum of first n terms of an AP is


Sn = [2a + (n - 1)d]


Sum of 23 terms is given by:


S23 = [2(5) + (23 - 1)(8)]


= (23/2) × [10 + 176]


= (23/2) × 186


= 23 × 93


= 2139


Thus, sum of 23 terms of this Arithmetic series is 2139.

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