Solve the problem.
-A pendulum bob swings through an arc 40 inches long on its first swing. Each swing thereafter, it swings only $86 \%$ as far as on the previous swing. What is the length of the arc after 11 swings? Round your answer to two decimal places, if necessary.
A) $7.61 \mathrm { in }$.
B) $344 \mathrm { in }$.
C) $8.85 \mathrm { in } .$
D) $6.55 \mathrm { in } .$

Question

Quizplus · Accepted Answer

The length of the arc after 11 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, $a_1 = 40$ inches, $r = 0.86$, and $n = 11$. So, $a_{11} = 40 \cdot 0.86^{(11-1)} = 40 \cdot 0.86^{10} \approx 8.85$ inches.

Solve the Problem 86%86 \%86% As Far as on the Previous Swing

Solve the Problem $86 \%$ As Far as on the Previous Swing