Answer
General term: $a_{n}=\frac{486}{3^{n−1}}$
First $5$ terms: $486,162,54,18,6$
It takes $6$ bounces for the ball to rebound less than 1 foot.
Work Step by Step
Given,
$a_{1}=486$
$r=\frac{1}{3}$
Geometric Sequence Formula:
$a_{n}=a_1(r)^{n−1}$
Substitute $a_{1}$ and $r$ into the formula to find the general term.
$a_{n}=\frac{486}{3^{n−1}}$
First $5$ terms:
$486,162,54,18,6$
Next few terms:
$2,\frac{2}{3}$
Since the first term in the sequence is the height before the ball has bounced, the counter for the number of bounces starts on the second term. Therefore, it takes $6$ bounces for the ball to rebound less than 1 foot.
