There are n A.M.s between 3 and 17. The ratio of the last mean to the first mean is 3 : 1. Find the value of n.

Question

Philoid · Accepted Answer

Let the series be 3, A₁, A₂, A₃, ........, A_n, 17

From the data,

We know total terms in AP are n + 2

So 17 is the (n + 2)th term

We know,

A_n = a + (n - 1)d

So, 17 = 3 + (n + 2 - 1)d

Therefore,

And

Since,

9n + 51 = 17n + 3

8n = 48

n = 6

There are 6 terms in AP