Q. 63.7( 6 Votes )

Insert A.M.s between 7 and 71 in such a way that the 5th A.M. is 27. Find the number of A.M.s.

Answer :

Let the series be 7, A1, A2, A3, ........, An, 71


We know total terms in AP are n + 2


So 71 is the (n + 2)th term


We know,


An = a + (n - 1)d


So, A6 = a + (6 - 1)d


a + 5d = 27 (5th term)


d = 4


71 = (n + 2)th term


71 = a + (n + 2 - 1)d


71 = 7 + n(4)


n = 15


There are 15 terms in AP


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