# How do you find the missing terms in the geometric sequence 32, __, 72, __, 162?

Nov 12, 2015

Here is the sequence:

$32 , 48 , 72 , 108 , 162$

#### Explanation:

In a geometric series, we go from one term to another by multiplying by some number $r$. So if we call our first missing term $x$, we know the following:
$32 \cdot r = x$
$x \cdot r = 72$
substitute to find the following...
$32 \cdot r \cdot r = 72$

${r}^{2} = \frac{72}{32}$
${r}^{2} = \frac{9}{4}$
$r = \frac{3}{2}$

now we can find the two missing terms...
$32 \cdot \frac{3}{2} = 48$
$72 \cdot \frac{3}{2} = 108$