Answer
$a_1 = 1$
$a_2 = 5$
$a_3 = 11$
$a_4 = 19$
$a_5 = 29$
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 $a_1 = 1$, so we need to come up with the next four terms of the sequence, $a_2$ through $a_5$:
For $n = 2$:
$a_2 = a_{2 - 1} + 2(2)$
Simplify:
$a_2 = a_{1} + 4$
Substitute $a_1 = 1$ into the formula:
$a_2 = 1 + 4$
Add:
$a_2 = 5$
For $n = 3$:
$a_3 = a_{3 - 1} + 2(3)$
Simplify:
$a_3 = a_{2} + 6$
Substitute $a_2 = 5$ into the formula:
$a_3 = 5 + 6$
Add:
$a_3 = 11$
For $n = 4$:
$a_4 = a_{4 - 1} + 2(4)$
Simplify:
$a_4 = a_{3} + 8$
Substitute $a_3 = 11$ into the formula:
$a_4 = 11 + 8$
Add:
$a_4 = 19$
For $n = 5$:
$a_5 = a_{5 - 1} + 2(5)$
Simplify:
$a_5 = a_{4} + 10$
Substitute $a_4 = 19$ into the formula:
$a_5 = 19 + 10$
Add:
$a_5 = 29$
