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

1.	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, A₁, A₂, A₃, ........, 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, A₆ = 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.

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, A₁, A₂, A₃, ........, 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,

A₆ = 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.