Question

In a G.P., the 4^th term is 48 and 7^th term is 384. Find its 6^th term.

Answer 1

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 G.P. = 48

⇒ a₄ = 48

⇒ ar^{4 − 1} = 48

⇒ ar³ = 48 ..........(1)

Given,

7^th term of G.P. = 384

⇒ a₇ = 48

⇒ ar^{7 − 1} = 384

⇒ ar⁶ = 384 ..........(2)

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

⇒ `(ar^6)/(ar^3)​ = 384/48`

⇒ r³ = 8

⇒ r³ = 2³

⇒ r = 2

Substituting value of r in equation (1), we get:

⇒ a(2)³ = 48

⇒ a × 8 = 48

⇒ a = `48/8​` = 6.

⇒ a₆ = ar^{6 − 1}

⇒ a₆ = ar⁵

⇒ a₆ = 6 × 2⁵

⇒ a₆ = 6 × 32

⇒ a₆ = 192.

Hence, 6^th term of G.P. = 192.