find the ratio of an infinite geometric series if the sum is 2 and the first term is 0.5

Question

help me to find the right solution

Answer 1

The formula for the sum of an infinite geometric series is:

 

S = a₀ / (1 - r)

 

S is the sum

a₀ is the first term

r is the ration

 

The sum is 2, and the first term is 0.5, so plug in what you know and see what you come up with:

 

2 = 0.5 / (1 - r)

 

That's an equation you can solve:

 

2(1 - r) = 0.5

1 - r = 0.5 / 2 = 0.25

0.75 - r = 0

0.75 = r

 

So the ratio is 0.75.