The sum to infinity of a geometric series with first term a and common ratio r is 10. The sum to infinity of a second geometric series with first term a and common ratio 2r is 15.

a] find the value of r. [4]

b] find the sum of the first four terms of the series, giving your answer correct to two decimal places. [3]

Part b I will be okay with, just the first part is the trouble here.

I got two simultaneous equations from it:

10 - 10r = a - (1)

15 - 30r = a - (2)

Putting them together, I got 5 + 20r = a

Or, 5 (1 + 4r) = a, whichever is preferred.

So this means (if I'm right) that $\displaystyle \frac{a}{1 + 4r}$ = 5.

If this is right, where do I go from here?

If it is wrong, please could you help me?