An infinite geometric series has a first term ai = 15 and a sum of 45. Explain how you can use the formula S = 1, to find the value of the common ratio. What is the value of r?

r=

Step-by-step explanation:

The sum to infinity of a geometric series is calculated as

S∞ = ; | r | < 1

where a₁ is the first term and r the common ratio

here a₁ = 15 and S∞ = 45 , then

45 = ( multiply both sides by (1 - r ) )

45(1 - r) = 15 ( divide both sides by 45 )

1 - r = = ( subtract 1 from both sides )

- r = - 1 = - ( multiply both sides by - 1 )

r =