Find the geometric progression whose 5^th term is 48 and 8^th term is 384.

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

By formula,

⇒ a_n = ar^{n - 1}

⇒ a₅ = ar^{5 - 1}

⇒ 48 = ar⁴ ……..(1)

⇒ a₈ = 384

⇒ ar^{8 - 1} = 384

⇒ ar⁷ = 384 ……..(2)

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

$\Rightarrow \dfrac{ar^7}{ar^4} = \dfrac{384}{48} \\[1em] \Rightarrow r^3 = 8 \\[1em] \Rightarrow r^3 = (2)^3 \\[1em] \Rightarrow r = 2.$

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

⇒ a(2)⁴ = 48

⇒ 16a = 48

⇒ a = $\dfrac{48}{16}$ = 3.

G.P. = a, ar, ar², ………

= 3, 3 × 2, 3 × 2², ……..

= 3, 6, 12, ……

Hence, G.P. = 3, 6, 12, ……