Q. 314.7( 29 Votes )

Determine the nth term of the AP whose 7th term is - 1 and 16th term is 17.

Answer :

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

Given: a7 = - 1


a16 = 17


Now, Consider a7 = - 1


a + (7 - 1)d = - 1


a + 6d = - 1 ……….(1)


Consider a16 = 17


a + (16 - 1)d = 17


a + 15d = 17 ……….(2)


Now, subtracting equation (1) from (2), we get,


9d = 18


d = 2


from equation (1), we get,


a = - 1 - 6d


a = - 1 - 6 × (2)


a = - 1 - 12


a = - 13


Now, the nth term of the AP is given by:


an = a + (n - 1)d


an = - 13 + (n - 1) × 2


an = 2n - 15


nth term of the AP is (2n - 15)


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