[100 + C] / [60 + C] = [160 + C] / [100 + C], solve for C
Cross Multiply
[100 + C]^2 = [60 + C) * [160 + C]
C^2 + 200 C + 10000 = C^2 + 220 C + 9600
C^2 - C^2 + 200C - 220C ==9600 - 10000
- 20C =- 400
C == - 400 / - 20 = 20
So, the GS would look like this:
[60 + 20], [100 + 20], [160 + 20] = 80, 120, 180
First term = 80 and Common ratio = 120 / 80 = 1.5