Question

The fourth term of a Geometric Progression (G.P.) is 16 and its seventh term is 128. Find its:

1. common ratio
2. first term

Answer 1

(a) We know that,

a_n = ar^{n − 1}

Given: a₄ = ar³ = 16    ...(1)

a₇ = ar⁶ = 128    ...(2)

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

⇒ `(ar^6)/(ar^3) = 128/16`

⇒ r³ = 8

⇒ r = `3sqrt8`

⇒ r = 2

Hence, common ratio = 2.

(b) The first term,

Substituting r = 2 in equation (1), we get :

⇒ a(2)³ = 16

⇒ a(8) = 16

⇒ a = `16/8`

⇒ a = 2

Hence, first term = 2.