Question 1184228: If 64, 27 and 36 are the Pth, Qth and Rth term of geometric sequence. Find the value of P + 2Q?
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
There is some good basic mathematics involved in trying to solve this problem.
Unfortunately, the problem is very poorly stated, leaving the possibility for multiple answers -- in fact an infinite number of possible answers....
First put the numbers in increasing order: 27, 36, 64.
Then find the ratio of consecutive numbers in that list:
36/27 = 4/3
64/36 = 16/9 = (4/3)^2
So one possibility is that the common ratio for the geometric sequence is 4/3, and four consecutive terms of the sequence are 27, 36, 48, and 64.
But there is nothing in the statement of the problem that tells us whether those would be terms 1 through 4, or terms 2 through 5, or terms 24 through 27, or....
Furthermore, the given three numbers might be terms of a geometric series with common ratio (4/3)^(1/2) -- or even (4/3)^(1/5).
Finally, it is possible that the sequence is decreasing, with four terms of 64, 48, 36, and 27. And in that case the common ratio could be 3/4, or (3/4)^(1/7), etc....
Obviously the values of P, Q, and R depend on which geometric sequence you choose; therefore the question cannot be answered.
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