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.
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