Answer
$a_n=5(-\dfrac{14}{5})^{n-1}$ and $a_7= 2409.45$
Work Step by Step
The given series shows a geometric series with a common ratio $5r=-14 $
Thus, $r=-\dfrac{14}{5}$
The nth term is given by $a_n= a_1 r^{n-1}$
This gives: $a_n=5(-\dfrac{14}{5})^{n-1}$
Plug in $n=7$
$a_7=5(-\dfrac{14}{5})^{7-1} \approx 2409.45$
Hence, $a_n=5(-\dfrac{14}{5})^{n-1}$ and $a_7= 2409.45$
