# 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

**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.