Answer
The equation for the $n$th term is
$a_n=224(\frac{1}{2})^{n-1}$
and $a_6=7$
Work Step by Step
Write down the series from the graph.
$224,112,56,28,...$
First term $a_1=224$.
Common ratio $r=\frac{112}{224}=\frac{1}{2}$.
Equation for a geometric sequence is
$\Rightarrow a_n=a_1r^{n-1}$
Substitute $224$ for $a_1$ and $\frac{1}{2}$ for $r$.
$\Rightarrow a_n=224(\frac{1}{2})^{n-1}$
Substitute $6$ for $n$.
$\Rightarrow a_6=224(\frac{1}{2})^{6-1}$
Simplify.
$\Rightarrow a_6=224(\frac{1}{2})^{5}$
$\Rightarrow a_6=7$.
