Which term of the G.P. 5, 10, 20, 40,…… is 640?

Given,

The G.P. : 5, 10, 20, 40,……

a = 5

r = $\dfrac{10}{5}$ = 2

Let nth term be 640.

T_n = 640

We know that,

nth term of a G.P. is given by,

T_n = ar^{n - 1}

⇒ 640 = (5).2^{n - 1}

⇒ $\dfrac{640}{5}$ = 2^{n - 1}

⇒ 128 = 2^{n - 1}

⇒ 2⁷ = 2^{n - 1}

Equating the exponents:

⇒ 7 = n - 1

⇒ n = 7 + 1

⇒ n = 8.

Hence, 8th term of G.P. is 640.