When the same constant is added to the numbers 60, 100 and 165 a three-term geometric sequence arises. What is the common ratio of the resulting sequence?
We can solve this
[100 + x ] / [ 60 + x] = [ 165 + x ] / [100 + x]
[100 + x]^2 = [ 60 + x ] [ 165 + x ]
x^2 + 200x + 10000 = x^2 + 225x + 9900
10000 - 9900 = 25x
100 = 25x
x = 100 / 25 = 4
Check
104 / 64 = 13 / 8
169 / 104 = 13 / 8
r =13 / 8
+212 
