Question

The 4^th term of a G.P. is 54 and its 7^th term is 1458, the common ratio of this G.P is ______.

Options

• `1/3`

• 3

• −3

• `-1/3`

Answer 1

The 4^th term of a G.P. is 54 and its 7^th term is 1458, the common ratio of this G.P is 3.

Explanation:

Let first term of G.P. be a and common ratio be r.

By formula,

⇒ a_n = ar^{n − 1}

Given,

4^th term of a G.P. is 54.

⇒ a₄ = 54

⇒ ar^{4 − 1} = 54

⇒ ar³ = 54 .........(1)

7^th term of a G.P. is 1458.

⇒ a₇ = 1458

⇒ ar^{7 − 1} = 1458

⇒ ar⁶ = 1458 .........(2)

Dividing equation (2) by (1), we get:

⇒ `(ar^6)/(ar^3) = 1458/54`

⇒ r³ = 27

⇒ r³ = 33

⇒ r = 3