Solve the problem.
-After being struck with a hammer, a gong vibrates 54 vibrations in the first second and in each second thereafter makes $\frac { 6 } { 7 }$ 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's vibrations form a geometric series with the first term $a = 54$ and common ratio $r = \frac{6}{7}$. The sum $S$ of an infinite geometric series is given by $S = \frac{a}{1 - r}$, where $a$ is the first term and $r$ is the common ratio. Substituting the given values, $S = \frac{54}{1 - \frac{6}{7}} = \frac{54}{\frac{1}{7}} = 54 \times 7 = 378$.

Solve the Problem 67\frac { 6 } { 7 }76​ As Many Vibrations as in the Previous Second

Solve the Problem $\frac { 6 } { 7 }$ As Many Vibrations as in the Previous Second