Ive gotten to (60+x)/(100+x) = (100+x)(100+x).

Cross multiply to get 9600+x^2+200x = 10000 +200x + x^2.

Then 400 = 20x

The sequence is 80, 120, 180.

Then to find the common ratio, 120 divided by 80 is 3/2, and 180 divided by 3/2 is 120.

But it isn't right, and I can't find my mistake. Any help?

Blizzardshine Oct 1, 2022

#1**+1 **

and it's cut off in the title, it's supposed to be: 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?

Blizzardshine Oct 1, 2022