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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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