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The first and second terms of a geometric sequence have a sum of 15, while the second and third terms have a sum of 60. Use an algebraic method to find the three terms.

This is what I have so far:

a + b + c

a + b = 15

b + c = 60

a = a

r = b/a

S2 = 15 = a(1-(b/a)^2)/1-(b/a)

S3 = 60 = a(1-(b/a)^3)/1-(b/a)

I then solved for a and b and got a = 3.75 and b = 11.25.

After knowing a and b, I find the common ratio: 3. But my numbers do not work for S3 because I got 48.75:grumpy: (Which, interestly enough is 11.25 away from 60:uhh: )

I'm really confused

Thanks