# What is the 10th term of the geometric sequence 3, 12, 48, …?

Nov 26, 2015

The $10$th term is $786432$

#### Explanation:

A geometric sequence is a sequence of the form
$a , a r , a {r}^{2} , a {r}^{3} , \ldots$
where $a$ is an initial value and $r$ is a common factor between terms.

Looking at this, we can tell that the $n$th term will be of the form $a {r}^{n - 1}$ and so the $10$th term will be $a {r}^{9}$.

In the given sequence, we start at $3$ and thus $a = 3$.

To find $r$ we need only divide a term by the term prior to it. So, for example, dividing the second term by the first gives us

$r = \frac{a r}{a} = \frac{12}{3} = 4$

Thus the $10$th term is $3 \cdot {4}^{9} = 786432$