Question

The 8^th term of a G.P. is 192 and its common ratio is 2, then the first term of the G.P. is ______.

Options

• 3

• \[\frac{1}{3}\]

• \[\frac{2}{3}\]

• \[\frac{3}{2}\]

Answer 1

The 8^th term of a G.P. is 192 and its common ratio is 2, then the first term of the G.P. is `bbunderline(3/2)`.

Explanation:

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

By formula,

⇒ a_n = ar^{n − 1}

Given,

8^th term of a G.P. is 192.

⇒ a₈ = 192

⇒ ar^{8 − 1} = 192

⇒ ar⁷ = 192

Substituting value of common ratio (r) = 2 in above equation, we get:

⇒ a(2)⁷ = 192

⇒ 128a = 192

⇒ a `192/128`

⇒ a = `3/2`