Q. 374.2( 11 Votes )

The 17th term of AP is 5 more than twice its 8th term. If the 11th term of the AP is 43, find its nth term.

Answer :

Let a and d be the first term and common difference of the AP Given: a17 = 2 × a8 + 5

a11 = 43


To find: nth term = an


Consider a11 = 43


a + (11 - 1)d = 43


a + 10d = 43 ………….. (1)


Consider a17 = 2 × a8 + 5


a + (17 - 1)d = 2[a + (8 - 1)d] + 5


a + 16d = 2a + 14d + 5


- a + 2d = 5 ……………….(2)


Adding equation (1) and equation (2), we get


12d = 48


d = 4


from equation (1), we get,


a = 43 - 10d


= 43 - 40


= 3


Now, nth term is given by:


an = a + (n - 1)d


an = 3 + (n - 1)4


an = 4n - 1


Therefore, nth term is given by (4n - 1).


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