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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?


Sagot :

Answer:

r= [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

The sum to infinity of a geometric series is calculated as

S∞ = [tex]\frac{a_{1} }{1-r}[/tex] ; | r | < 1

where a₁ is the first term and r the common ratio

here a₁ = 15 and S∞ = 45 , then

45 = [tex]\frac{15}{1-r}[/tex] ( multiply both sides by (1 - r ) )

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

1 - r = [tex]\frac{15}{45}[/tex] = [tex]\frac{1}{3}[/tex] ( subtract 1 from both sides )

- r = [tex]\frac{1}{3}[/tex] - 1 = - [tex]\frac{2}{3}[/tex] ( multiply both sides by - 1 )

r = [tex]\frac{2}{3}[/tex]

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