Find the 8^th term of a G.P., if its common ratio is 2 and 10^th term is 768.

Given,

Common ratio (r) = 2

By formula,

⇒ a_n = ar^{n - 1}

Given,

10^th term of G.P. = 768

⇒ a₁₀ = 768

⇒ ar^{10 - 1} = 768

⇒ ar⁹ = 768

⇒ a × 2⁹ = 768

⇒ a × 512 = 768

⇒ a = $\dfrac{768}{512} = \dfrac{3}{2}$.

8th term of G.P. is given by :

⇒ a₈ = ar^{8 - 1}

⇒ a₈ = ar⁷

⇒ a₈ = $\dfrac{3}{2} \times 2^7$

⇒ a₈ = 3 × 2⁶

⇒ a₈ = 3 × 64 = 192.

Hence, 8^th term of a G.P. is given by 192.