Answer
$a_1 =1$
$a_2 = 4$
$a_3 =1$
$a_4 = 4$
$a_5 =1$
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 four terms of the sequence, $a_2$ through $a_5$:
For $n = 2$:
$a_2 = 5 - a_{2 - 1}$
Simplify:
$a_2 = 5 - a_{1}$
Substitute $a_1 = 1$ into the formula:
$a_2 = 5 - 1$
Subtract:
$a_2 = 4$
For $n = 3$:
$a_3 = 5 - a_{3 - 1}$
Simplify:
$a_3 = 5 - a_{2}$
Substitute $a_2 = 4$ into the formula:
$a_3 = 5 - 4$
Subtract:
$a_3 =1$
For $n = 4$:
$a_4 = 5 - a_{4 - 1}$
Simplify:
$a_4 = 5 - a_{3}$
Substitute $a_3 = 1$ into the formula:
$a_4 = 5 - 1$
Subtract:
$a_4 = 4$
For $n = 5$:
$a_5 = 5 - a_{5 - 1}$
Simplify:
$a_5 = 5 - a_{4}$
Substitute $a_4 = 4$ into the formula:
$a_5 = 5 - 4$
Subtract:
$a_5 =1$
