Given that $a$ is a real number and $a, 2a, 8$ form a geometric sequence, find the value of $a$.

1. Problem Description

Given that $a$ is a real number and $a, 2a, 8$ form a geometric sequence, find the value of $a$.

2. Solution Steps

In a geometric sequence, the ratio between consecutive terms is constant. Therefore, we have:

$\frac{2a}{a} = \frac{8}{2a}$

Assuming $a \neq 0$, we can simplify the left side of the equation:

$2 = \frac{8}{2a}$

Multiply both sides by $2a$:

$4a = 8$

Divide both sides by 4:

$a = 2$

If $a = 0$, then the sequence is $0, 0, 8$. However, the ratio between terms is not constant, so $a$ cannot be

0.

3. Final Answer

$a = 2$

The answer is B.