Two infinite geometric series a + ar + ar^2 + ... and b + br + br^2 + ... have the same sum. Also, the second term of the second series is the first term of the first series. if r = 1/2 for the second series, find r for the first series.

I got that the rate (r) of the first series is 2/3. Is this correct??

a/(1-r) = b/(1-1/2)

a = br

r/(1-r) = 2

r = 2/3

thanks