Question

When the same constant is added to the numbers 60, 100, and 180, a three-term geometric sequence arises. What is the common ratio of the resulting sequence?

Answer 1

Answer: 2

Explanation:

Let the constant be
`a`. Then, it follows that:

`(100+a)/(60+a)=(180+a)/(100+a)\\\\(100+a)^2=(60+a)(180+a)\\\\a^2 +200a+10000=a^2 +240a+10800\\\\200a+10000=240a+10800\\\\40a=-800\\\\a=-20\\\\\therefore r=(100-20)/(60-20)=2`