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# This is very similar to a previous question.

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When the same constant is added to the numbers 60, 100, and 160 a three-term geometric sequence arises. What is the common ratio of the resulting sequence?

Aug 29, 2022

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When the same constant is added to the numbers 60, 100, and 160 a three-term geometric sequence arises. What is the common ratio of the resulting sequence?

$$\frac{100+n}{60+n}=\frac{160+n}{100+n}\\ (100+n)^2=(60+n)(160+n)\\ 10000+n^2+200n=9600+n^2+220n\\ 400=20n\\ n=20\\$$

so the sequence is    80,120, 180

120/80 = 3/2

180/120=3/2

Common ratio is 3/2

Aug 29, 2022
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Thanks so much Melody,

I really appreciate it!

Aug 29, 2022
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Thanks for the feedback :)

And you are welcome.

Melody  Aug 30, 2022