Question

Use the formula to evaluate the infinite series. Round your answer to the nearest hundredth if necessary. 72 + 12 + 2 + . . . Formula for a converging infinite series. a1 is the first term and r is the common ratio. 86.4 14.4 6 432

Answer 1

The first term is a = 72

The common ratio is r = 1/6.
We multiply each term by 1/6, which is the same as dividing each term by 6.
To find r, divide any term you want over the previous term
r = 12/72 = 1/6
r = 2/12 = 1/6
etc.

Now use the infinite sum formula to find S
S = infinite sum
S = a/(1-r) ... see note below
S = 72/(1-1/6)
S = 72/(6/6 - 1/6)
S = 72/(5/6)
S = (72/1) divided by (5/6)
S = (72/1)*(6/5)
S = (72*6)/(1*5)
S = 432/5
S = 86.4

Answer: 86.4

note: this infinite sum formula only works if -1 < r < 1. In the case of r = 1/6 = 0.167 (approx), this r value is between -1 and 1.