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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?

 Nov 30, 2022
 #1
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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 \(\boxed{1/2}\) 

 Nov 30, 2022

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