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

Guest Aug 29, 2022

#1**+3 **

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

Melody Aug 29, 2022