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?
\(\phantom{60, 100, and 160}\)
(100 + N) / (60+N) = (180 + N) / (100 + N)
(100 + N)^2 = (180 + N) (60 + N)
10000 + 200N + N^2 = 10800 + 240N + N^2
200N - 240N = 10800 - 10000
-40N = 800
N = 800 / -40 = -20
Common Ratio = (100 -20) / (60 - 20) = 80 / 40 = 2