**Okay so first some definitions**

**Geometric sequence and common ratio. A geometric sequence a sequence where the next number is the previous number multiplied by the same number as in the whole seequence a.k.a a common ratio.**

**equation:**

** \(\frac{150+c}{120+c}=\frac{120+c}{60+c}=x\)**

**\(\)**

**okay so we want to find what x is.**

**solve: find common denominators**

**\(9000+210c+c^2 = 14400+240c+c^2\)**

**\(30c=-5400\) , so\(c=-180\). **

**Now we get x = 1/2 \(so\) yeah**

**TO CHECK: **

**plug x back in to the equations to that it is correct! I hope you got it so the common ratio is \(\boxed{1/2}\) **