Answer
The sequence is $-36,-18,-9,-4.5,-2.25,-1.125,...$
The graph is shown below.
Work Step by Step
First term $a_1=-36$
Recursive equation $a_n=\frac{1}{2}a_{n-1}$
Use the recursive equation to find the next five terms.
$\Rightarrow a_2=\frac{1}{2}a_{2-1}=\frac{1}{2}a_{1}=\frac{1}{2}(-36)=-18$
$\Rightarrow a_3=\frac{1}{2}a_{3-1}=\frac{1}{2}a_{2}=\frac{1}{2}(-18)=-9$
$\Rightarrow a_4=\frac{1}{2}a_{4-1}=\frac{1}{2}a_{3}=\frac{1}{2}(-9)=-4.5$
$\Rightarrow a_5=\frac{1}{2}a_{5-1}=\frac{1}{2}a_{4}=\frac{1}{2}(-4.5)=-2.25$
$\Rightarrow a_6=\frac{1}{2}a_{6-1}=\frac{1}{2}a_{5}=\frac{1}{2}(-2.25)=-1.125$
Use table to organize the terms.
Plot the ordered pairs $(n,a_n)$.
