Question

What is the number of the terms of geometrical sequence if its first, fourth and the last term is equal to 2, 54 and 486 respectively.

Answer 1

The number of terms of the G.P. is 6

Explanation:

Let the G.P. has first term a, common ratio r and the number of terms n.

The G.P. has first term 2, so a = 2.

Now, the fourth term is 54 i.e. ar³ = 54

⇒ 2r³ = 54

⇒ r³ = 27

⇒ r = 3

Now, the last term i.e. the nth term is=
`ar^(n - 1) = 486`

⇒
`2 * 3^(n - 1) = 486`

⇒
`3^(n - 1) = 243 = 3^(5)`

Hence, (n - 1) = 5

⇒ n = 6

So the number of terms of the G.P. is 6 (Answer)