Answer
The sequence is $80,-40,20,-10,5,-\frac{5}{2},...$
The graph is shown below.
Work Step by Step
First term $a_1=80$
Recursive equation $a_n=-\frac{1}{2}a_{n-1}$
Use the recursive equation to find the next five terms.
$\Rightarrow a_2=-\frac{1}{2}a_{2-1}=-\frac{1}{2}a_1=-\frac{1}{2}(80)=-40$
$\Rightarrow a_3=-\frac{1}{2}a_{3-1}=-\frac{1}{2}a_2=-\frac{1}{2}(-40)=20$
$\Rightarrow a_4=-\frac{1}{2}a_{4-1}=-\frac{1}{2}a_3=-\frac{1}{2}(20)=-10$
$\Rightarrow a_5=-\frac{1}{2}a_{5-1}=-\frac{1}{2}a_4=-\frac{1}{2}(-10)=5$
$\Rightarrow a_6=-\frac{1}{2}a_{6-1}=-\frac{1}{2}a_5=-\frac{1}{2}(5)=-\frac{5}{2}$
Use table to organize the terms.
Plot the ordered pairs $(n,a_n)$.
