Find the common ratio for the following geometric sequence? 0.75, 1.5, 3, 6, . . .

3 1.5 2 0.75

Apr 19, 2017

$r = 2$

Explanation:

A geometric sequence can be written in the form:
$\left\{a , a \cdot r , a \cdot {r}^{2} , a \cdot {r}^{3} , \ldots a \cdot {r}^{n - 1} , \ldots\right\}$, where $r$ is the common ratio.

$r = \frac{1.5}{.75} = \frac{3}{1.5} = \frac{6}{3} = 2$

Check:
$\left\{.75 , .75 \cdot 2 = 1.5 , .75 \cdot {2}^{2} = 3 , .75 \cdot {2}^{3} = 6 , \ldots\right\}$

Apr 19, 2017

$r = 2$

Explanation:

$\text{the standard geometric sequence is.}$

$a , a r , a {r}^{2} , a {r}^{3} , \ldots \ldots . . , a {r}^{n - 1}$

$\text{where r is the common ratio}$

$r = \frac{{a}_{2}}{{a}_{1}} = \frac{{a}_{3}}{{a}_{2}} = \ldots \ldots = \frac{{a}^{n}}{{a}^{n - 1}}$

$\Rightarrow r = \frac{1.5}{0.75} = \frac{3}{1.5} = 2$