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The sum of first n terms of an arithmeti...

The sum of first n terms of an arithmetic progression is 270. If common difference of the arithmetic progression is 2 and the first term is an integer, then number of possible values of `n gt 2` is

A

15

B

14

C

13

D

16

Text Solution

Verified by Experts

The correct Answer is:
B
`270 = n/2[2a +(n-1)2]`
`rArr 270 =n(a + n-1)`
`rArr 2 xx 3^(3) xx 5 = n(a+n-1)`
Number of possible value of n
`=(1+1) (3+1) (1+1)-1-1`
=14
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