Can anyone help with this problem?
When the same constant is added to the numbers 60, 120, and 150 a three-term geometric sequence arises. What is the common ratio of the resulting sequence?
+297 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 \(\boxed{1/2}\)
