How many terms of the series 1+3+5+…….. must be taken

How many terms of the series 1+3+5+…….. must be taken in order so that the sum may be 19600?
(a) 140
(b) 120
(c) 240
(d) 150

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1 Answer(s)

Answer: (a) 140 

Solution:-
Given series – 
1 + 3 + 5 + ………………. 
First term (a) = 1
Difference (d) = 3 – 1
 = 2, 

Formula-
The sum of n term (S) n = n {2 a + (n – 1) d}/2 

Then, 19600 = n { 2 x 1 + (n – 1) x 2}/2
 19600 = n {2 + 2 n – 2}/2 
19600 = n (2 n)/2
19600 = n^2 
Square root both side, 
140 = n 
Then, the number of terms in the series is 140. 

Hence, the correct answer is option (a) 140. 

Anurag Mishra Professor Answered on 4th May 2016.
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