Q. 63.7( 6 Votes )

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

Answer :

Let the series be 7, A_{1}, A_{2}, A_{3}, ........, A_{n}, 71

We know total terms in AP are n + 2

So 71 is the (n + 2)th term

We know,

A_{n} = a + (n - 1)d

So, A_{6} = a + (6 - 1)d

a + 5d = 27 (5^{th} 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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