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

2 Answers
Jan 10, 2016

Answer:

#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

Answer:

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.