The problem asks to find the value of $a_4$ in a geometric sequence $\{a_n\}$, given that $a_1 = 2$ and $a_2 = 4$.

1. Problem Description

The problem asks to find the value of $a_4$ in a geometric sequence $\{a_n\}$, given that $a_1 = 2$ and $a_2 = 4$.

2. Solution Steps

In a geometric sequence, the ratio between consecutive terms is constant. Let's denote this common ratio as $r$.

We have

$r = \frac{a_2}{a_1} = \frac{4}{2} = 2$.

The formula for the $n$-th term of a geometric sequence is given by

$a_n = a_1 \cdot r^{n-1}$.

We want to find $a_4$, so we have

$a_4 = a_1 \cdot r^{4-1} = a_1 \cdot r^3$.

Substituting the given values, we get

$a_4 = 2 \cdot 2^3 = 2 \cdot 8 = 16$.

3. Final Answer

The final answer is

1

6. [D]