Question

How do you find the sum of the infinite geometric series 72 + 12 + 2 + +… ?

Answer 1

`432/5 = 84 2/5`

Explanation:

The formula for the sum of an infinite series is `S = a/(1-r)`
where r is the common ratio and a is the first term.

Therefore, `S = 72/(1-1/6)=72/(5/6)=432/5`

Answer 2

First, you must find the common ratio, r, of the series.

Explanation:

r = `t_2 / t_1`

r = `12/72`

r = `1/6`

`S_∞` = `a/(1 - r)`

`S_∞` = `72/(1 - 1/6)`

`S_∞` = `72/(5/6)`

`S_∞`= `(72 • 6)/ 5`

`S_∞` = `432/5` or 146.4

The sum is `432/5` or 146.4. Hopefully you understand now!

Below I have posted one problem for your practice.

1. Find the wanted information.

a) An infinite geometric series has a third term of 18 and a common ratio of `1/2`. Find it's sum.

b) A pendulum has a first swing of 186 centimeters and a second swing of 124 centimetres. Assuming the pendulum swings forever, find the total distance travelled, rounded to the closest hundredth when necessary.