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# plz help

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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