Choose the one alternative that best completes the statement or answers the question.
-After being struck with a hammer, a gong vibrates 54 vibrations in the first second and in each second thereafter makes 67 as many vibrations as in the previous second. Find how many vibrations the gong makes before it
Stops vibrating.
A) 388 vibrations
B) 63 vibrations
C) 58 vibrations
D) 378 vibrations

Question

Quizplus · Accepted Answer

The gong vibrates 54 times in the first second. In each subsequent second, it vibrates 67% (or 0.67 times) of the previous second's vibrations. This forms a geometric series where the first term a = 54 and the common ratio r = 0.67. The sum of an infinite geometric series is given by S = a / (1 - r). Plugging in the values, S = 54 / (1 - 0.67) = 54 / 0.33 = 378 vibrations.

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