# How do you find the next two terms of the geometric sequence 16, 24, 36, ...?

Nov 9, 2016

The fourth and firth terms are $54$ and $81$

#### Explanation:

The common ratio from one term to the next is:
$\textcolor{w h i t e}{\text{XXX}} \frac{24}{16} = \frac{36}{24} = \frac{3}{2}$

Given:
$\textcolor{w h i t e}{\text{XXX}} {a}_{1} = 16$

$\textcolor{w h i t e}{\text{XXX}} {a}_{2} = 16 \times \frac{3}{2} = 24$ (as given)

$\textcolor{w h i t e}{\text{XXX}} {a}_{3} = 24 \times \frac{3}{2} = 36$ (as given)

$\textcolor{w h i t e}{\text{XXX}} {a}_{4} = 36 \times \frac{3}{2} = 54$

$\textcolor{w h i t e}{\text{XXX}} {a}_{5} = 54 \times \frac{3}{2} = 81$