Answer
The sequence is $-7,28,-112,448,-1792,7168,...$
The graph is shown below.
Work Step by Step
First term $a_1=-7$
Recursive equation $a_n=-4a_{n-1}$
Use the recursive equation to find the next five terms.
$\Rightarrow a_2=-4a_{2-1}=-4a_1=-4(-7)=28$
$\Rightarrow a_3=-4a_{3-1}=-4a_2=-4(28)=-112$
$\Rightarrow a_4=-4a_{4-1}=-4a_3=-4(-112)=448$
$\Rightarrow a_5=-4a_{5-1}=-4a_4=-4(448)=-1792$
$\Rightarrow a_6=-4a_{6-1}=-4a_5=-4(-1792)=7168$
Use table to organize the terms.
Plot the ordered pairs $(n,a_n)$.
The sequence is $-7,28,-112,448,-1792,7168,...$
The graph is shown below.
