Answer
The sequence is $2,6,18,54,162,486,...$
The graph is shown below.
Work Step by Step
First term $a_1=2$
Recursive equation $a_n=3a_{n-1}$
Use the recursive equation to find the next five terms.
$\Rightarrow a_2=3a_{2-1}=3a_1=3(2)=6$
$\Rightarrow a_3=3a_{3-1}=3a_2=3(6)=18$
$\Rightarrow a_4=3a_{4-1}=3a_3=3(18)=54$
$\Rightarrow a_5=3a_{5-1}=3a_4=3(54)=162$
$\Rightarrow a_6=3a_{6-1}=3a_5=3(162)=486$
Use table to organize the terms.
Plot the ordered pairs $(n,a_n)$.
