Find the number of terms of a G.P. whose first term is $\dfrac{3}{4},$ common ratio is 2 and the last term is 384.

Let the number of terms be n.

Given, a = $\dfrac{3}{4}$, r = 2 and a_n = 384.

By formula, a_n = ar^{n - 1}.

$\Rightarrow 384 = \dfrac{3}{4}(2)^{n - 1} \\[1em] \Rightarrow \dfrac{384 \times 4}{3} = (2)^{n - 1} \\[1em] \Rightarrow (2)^{n - 1} = 512 \\[1em] \Rightarrow (2)^{n - 1} = (2)^9 \\[1em] \Rightarrow n - 1 = 9 \\[1em] \Rightarrow n = 10.$

Hence, the number of terms in the G.P. are 10.