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

2 Answers
Jan 10, 2016

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

Jan 10, 2016

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.