Question 1209374: When the same constant is added to the numbers a, b, and c, a three-term geometric sequence arises. If a = 60, b = 120, and c = 150, what is the common ratio of the resulting sequence?
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! The n-th term of a geometric sequence is a_n = a_1*r^(n-1), where a_1 is the first term and r is the common ratio. Let x = the constant added to all the terms of the 3 term sequence. Thus, a_1 = 60 + x, a_2 = 120 + x, a_3 = a_3 + x
The ratios a_2/a_1 = a_3/a_2 = r -> (150+x)/(120+x) = (120+x)/(60+x). For simplicty, we divide the constant terms by 10.
Solving for x, we get:
90 + 21x + x^2 = 144 + 24x + x^2
-54 = 3x -> x = -18*10 = -180
So the terms are -120, -60, -30, and the common ratio = -60/-120 = 1/2
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