Solve the problem.
-After being struck with a hammer, a gong vibrates 20 vibrations in the first second and in each second thereafter makess $\frac { 2 } { 3 }$ as many vibrations as in the previous second. Find how many vibrations the gong makes before it
Stops vibrating.
A)30 vibrations
B)70 vibrations
C)25 vibrations
D)60 vibrations

Question

Quizplus · Accepted Answer

The gong's vibrations form a geometric series with the first term $a = 20$ and common ratio $r = \frac{2}{3}$. The sum 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, we get $S = \frac{20}{1 - \frac{2}{3}} = \frac{20}{\frac{1}{3}} = 60$ vibrations.

Solve the Problem 23\frac { 2 } { 3 }32​ As Many Vibrations as in the Previous Second

Solve the Problem $\frac { 2 } { 3 }$ As Many Vibrations as in the Previous Second