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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?

 

This question is very similar to what you guys answered here-https://web2.0calc.com/questions/when-the-same-constant-is-added-to-the-numbers-60-100-and-150-a-three-term-geometric-sequence-arises-what-is-the-constant-ratio-of-the-r

 Aug 29, 2022
 #1
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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
 #2
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Thanks so much Melody, 

I really appreciate it!

 Aug 29, 2022
 #3
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+1

Thanks for the feedback :)

And you are welcome. wink

Melody  Aug 30, 2022

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