Answer
$a_1 = 20$
$a_2 = 10$
$a_3 = 5$
$a_4 = \frac{5}{2}$
$a_5 = \frac{5}{4}$
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 $a_1 = 20$, so we need to come up with the next four terms of the sequence, $a_2$ through $a_5$:
For $n = 2$:
$a_2 = \frac{1}{2}a_{2 - 1}$
Simplify:
$a_2 = \frac{1}{2}a_{1}$
Substitute $a_1 = 20$ into the formula:
$a_2 = \frac{1}{2}(20)$
Multiply first:
$a_2 = \frac{20}{2}$
Simplify the fraction:
$a_2 = 10$
For $n = 3$:
$a_3 = \frac{1}{2}a_{3 - 1}$
Simplify:
$a_3 = \frac{1}{2}a_{2}$
Substitute $a_2 = 10$ into the formula:
$a_3 = \frac{1}{2}(10)$
Multiply first:
$a_3 = \frac{10}{2}$
Simplify the fraction:
$a_3 = 5$
For $n = 4$:
$a_4 = \frac{1}{2}a_{4 - 1}$
Simplify:
$a_4 = \frac{1}{2}a_{3}$
Substitute $a_3 = 5$ into the formula:
$a_4 = \frac{1}{2}(5)$
Multiply:
$a_4 = \frac{5}{2}$
For $n = 5$:
$a_5 = \frac{1}{2}a_{5 - 1}$
Simplify:
$a_5 = \frac{1}{2}a_{4}$
Substitute $a_4 = \frac{5}{2}$ into the formula:
$a_5 = \frac{1}{2}(\frac{5}{2})$
Multiply:
$a_5 = \frac{5}{4}$
