Answer
The equation for the $n$th term is
$a_n=7640(0.1)^{n-1}$
and $a_6=0.0764$
Work Step by Step
Write down the series from the table.
$7640,764,76.4,7.64,...$
First term $a_1=7640$.
Common ratio $r=\frac{764}{7640}=0.1$.
Equation for a geometric sequence is
$\Rightarrow a_n=a_1r^{n-1}$
Substitute $7640$ for $a_1$ and $0.1$ for $r$.
$\Rightarrow a_n=7640(0.1)^{n-1}$
Substitute $6$ for $n$.
$\Rightarrow a_6=7640(0.1)^{6-1}$
Simplify.
$\Rightarrow a_6=7640(0.1)^{5}$
$\Rightarrow a_6=0.0764$.
