Question

55. The sum of an infinite geometric series is five times the value of the first term. What is the common ratio of the series?

Answer 1

Answer:

r = 4/5

Step-by-step explanation:

Formula

Sum of an infinite geometric series = a / (1 - r)

Givens

Sum = 5*a

a = a

r = ?

Solution

5a = a/(1 - r)                   Divide both sides by a

5a/a = a / (a * (1 - r)       The a's on the right cancel

5 = 1 / (1 - r)                    Multiply both sides by 1 - r

5*(1 - r) = 1*(1 - r)/(1 - r)   The 1 - r s on the right cancel

5*(1 - r) = 1                     Remove the brackets.

5 - 5r = 1                        Subtract 5 from both sides

5-5 - 5r = 1 - 5               Combine

-5r = - 4                          Divide by - 5

r = 4/5