Question

An infinite geometric series has a first term ai = 15 and a sum of 45. Explain how you

Answer 1

Answer:

r= $\frac{2}{3}$

Step-by-step explanation:

The sum to infinity of a geometric series is calculated as

S∞ = $\frac{a_{1} }{1-r}$ ; | r | < 1

where a₁ is the first term and r the common ratio

here a₁ = 15 and S∞ = 45 , then

45 = $\frac{15}{1-r}$ ( multiply both sides by (1 - r ) )

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

1 - r = $\frac{15}{45}$ = $\frac{1}{3}$ ( subtract 1 from both sides )

- r = $\frac{1}{3}$ - 1 = - $\frac{2}{3}$ ( multiply both sides by - 1 )

r = $\frac{2}{3}$