If the $n^{th}$ term of a Geometric Progression (G.P.) is given by $5 \times 2^n$ then the common ratio is :

Given,

$$\begin{aligned}n^{th} \text{ term of the G.P.} = 5 \times 2^n \\[1em] \therefore t_n = 5 \times 2^n\end{aligned}$$

Replacing $n$ by $(n + 1)$, we get :

⇒ $t_{n + 1} = 5 \times 2^{n + 1}$

By formula,

$$\begin{aligned}\text{Common ratio } (r) = \frac{t_{n + 1}}{t_n} \\[1em] = \frac{5 \times 2^{n + 1}}{5 \times 2^n} \\[1em] = 2^{n + 1 - n} \\[1em] = 2.\end{aligned}$$

Hence, option 1 is the correct option.