Find the common ratio of an infinite geometric series with the given sum and first term

Question

S=9,a1=3

I need help with this Algebra 2 Problem please 

Answer 1

The sum of an infinite geometric series is:

 

S = a₁ / (1 - r)

 

S is the sum

a₁ is the first term

r is the common ratio

 

So all you have to do is plug in what you know and solve the resulting equation:

 

9 = 3 / (1 - r)

 

Divide both sides by 3:

3 = 1 / (1 - r)

 

Take the reciprocal of both sides:

1/3 = 1 - r

 

Add r to both sides:

r + 1/3 = 1

 

Subtract 1/3 from both sides:

r = 2/3

 

So the ratio is 2/3