Q. 94.0( 4 Votes )

The 7th term of an AP is – 1 and its 16th term is 17. The nth term of the AP is
A. (3n + 8)

B. (4n – 7)

C. (15 – 2n)

D. (2n – 15)

Answer :

Let a be the first term and d be the common difference.


Given: a7 = - 1


a16 = 17


Now, Consider a7 = - 1


a + 6d = - 1 …………(1)


Consider a16 = 17


a + 15d = 17 …………(2)


Subtract equation (1) from (2), we get,


9d = 18


d = 2


Common difference = d = 2


Now, from equation (1), we get,


a = - 1 - 6d


= - 1 - 6(2)


= - 13


Now, nth term of the AP is given by


an = a + (n - 1)d


= - 13 + (n - 1)2


= 13 + 2n - 2


= 2n - 15

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