# How do you find the indicated term of the geometric sequence where a_6=3, r=2, n=12?

Jun 22, 2017

${a}_{12} = \textcolor{red}{192}$

#### Explanation:

${a}_{6} = 3 = {a}_{5} \times r = {a}_{5} \times 2$
$\textcolor{w h i t e}{\text{XXX}} \rightarrow 3 = {a}_{5} \times 2$
$\textcolor{w h i t e}{\text{XXX}} \rightarrow {a}_{5} = \frac{3}{2}$

Similarly
$\textcolor{w h i t e}{\text{XXX}} {a}_{4} = \frac{3}{{2}^{2}}$
$\textcolor{w h i t e}{\text{XXX}} {a}_{3} = \frac{3}{{2}^{3}}$
$\textcolor{w h i t e}{\text{XXX}} {a}_{2} = \frac{3}{{2}^{4}}$
$\textcolor{w h i t e}{\text{XXX}} {a}_{1} = \frac{3}{{2}^{5}}$
$\textcolor{w h i t e}{\text{XXX}} {a}_{0} = \frac{3}{{2}^{6}}$

${a}_{n} = {a}_{0} \times {r}^{n}$
$\textcolor{w h i t e}{\text{XXX}} \rightarrow {a}_{12} = \frac{3}{{2}^{6}} \times {2}^{12}$
$\textcolor{w h i t e}{\text{XXXXXX}} = 3 \times {2}^{6}$
$\textcolor{w h i t e}{\text{XXXXXX}} = 2 \times 64$
$\textcolor{w h i t e}{\text{XXXXXX}} = 192$