Question

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 1

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

By using the formula,

A_n = a + (n – 1)d

A_n = 71, n = 6
A₆ = a + (6 – 1)d

a + 5d = 27 (5^th term)

d = 4

so,

71 = (n + 2)th term

71 = a + (n + 2 – 1)d

71 = 7 + n(4)

n = 15

∴ There are 15 terms in AP