# How do you write the first five terms of the geometric sequence a_1=5, r=2x?

Sep 27, 2017

$5 , 10 x , 20 {x}^{2} , 40 {x}^{3} , 80 {x}^{4}$

#### Explanation:

Given
$\textcolor{w h i t e}{\text{XXX}} {a}_{1} = 5$
By definition of geometric sequence
$\textcolor{w h i t e}{\text{XXX}} {a}_{n} = {a}_{n - 1} \times r$
Therefore
$\textcolor{w h i t e}{\text{XXX}} {a}_{2} = {a}_{1} \times r = 5 \times 2 x = 10 x$

$\textcolor{w h i t e}{\text{XXX}} {a}_{3} = {a}_{2} \times r = 10 \times 2 x = 20 {x}^{2}$

$\textcolor{w h i t e}{\text{XXX}} {a}_{4} = {a}_{3} \times r = 20 {x}^{2} \times 2 x = 40 {x}^{3}$

$\textcolor{w h i t e}{\text{XXX}} {a}_{5} = {a}_{4} \times r = 40 {x}^{3} \times 2 x = 80 {x}^{4}$