Solve.
-A pendulum bob swings through an arc 80 inches long on its first swing. Each swing thereafter, it swingsonly 66% as far as on the previous swing. What is the length of the arc after 9 swings? Round your answerto two decimal places, if necessary.
A)2.88 inches
B)1.9 inches
C)1.25 inches
D)422.4 inches

Question

Quizplus · Accepted Answer

The length of the arc after 9 swings can be found using the formula for the nth term of a geometric sequence, which is $a_n = a_1 \cdot r^{(n-1)}$, where $a_1$ is the first term, $r$ is the common ratio, and $n$ is the term number. Here, $a_1 = 80$ inches, $r = 0.66$, and $n = 9$. So, $a_9 = 80 \cdot 0.66^{(9-1)} = 80 \cdot 0.66^8 \approx 2.88$ inches.

Solve. -A Pendulum Bob Swings Through an Arc 80 Inches Long