Choose the one alternative that best completes the statement or answers the question.
-A pendulum bob swings through an arc 40 inches long on its first swing. Each swing thereafter, it swings only 63% as far as on the previous swing. What is the length of the arc after 9 swings? Round your answer to two
Decimal places, if necessary.
A) 0.63 inches
B) 201.6 inches
C) 0.39 inches
D) 0.99 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, $a_1 = 40$ inches, $r = 0.63$, and $n = 9$. So, $a_9 = 40 \cdot 0.63^{(9-1)} = 40 \cdot 0.63^8 \approx 0.99$ inches.

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