Solve the problem.
-After being struck with a hammer, a gong vibrates 32 vibrations in the first second and in each second thereafter makes $\frac { 4 } { 5 }$ as many vibrations as in the previous second. Find how many vibrations the gong makes before it stops vibrating.
A) 40 vibrations
B) 35 vibrations
C) 160 vibrations
D) 170 vibrations

Question

Quizplus · Accepted Answer

The vibrations form a geometric series with the first term $a = 32$ and common ratio $r = \frac{4}{5}$. The sum of an infinite geometric series is $S = \frac{a}{1-r}$. Substituting the values, $S = \frac{32}{1-\frac{4}{5}} = \frac{32}{\frac{1}{5}} = 160$.

Solve the Problem 45\frac { 4 } { 5 }54​ As Many Vibrations as in the Previous Second

Solve the Problem $\frac { 4 } { 5 }$ As Many Vibrations as in the Previous Second