Answer
$a_2 = 5$
$a_3 = 15$
$a_4 = 45$
$a_5 = 135$
$a_6 = 405$
Work Step by Step
In this exercise, we are given a recursive formula, which relates one term to the term before it.
We are given the initial term $a_1 = 2$, so we need to come up with the next five terms of the sequence, $a_2$ through $a_6$:
For $n = 2$:
$a_2 = 3a_{2 - 1}$
Simplify:
$a_2 = 3a_{1}$
Substitute $a_1 = 2$ into the formula:
$a_2 = 3(2)$
Multiply:
$a_2 = 5$
For $n = 3$:
$a_3 = 3a_{3 - 1}$
Simplify:
$a_3 = 3a_{2}$
Substitute $a_2 = 5$ into the formula:
$a_3 = 3(5)$
Multiply:
$a_3 = 15$
For $n = 4$:
$a_4 = 3a_{4 - 1}$
Simplify:
$a_4 = 3a_{3}$
Substitute $a_3 = 15$ into the formula:
$a_4 = 3(15)$
Multiply:
$a_4 = 45$
For $n = 5$:
$a_5 = 3a_{5 - 1}$
Simplify:
$a_5 = 3a_{4}$
Substitute $a_4 = 45$ into the formula:
$a_5 = 3(45)$
Multiply:
$a_5 = 135$
For $n = 6$:
$a_6 = 3a_{6 - 1}$
Simplify:
$a_6 = 3a_{5}$
Substitute $a_5 = 135$ into the formula:
$a_6 = 3(135)$
Multiply:
$a_6 = 405$
