Question 1190793: Find three numbers in GP such that their sum is 39 and their product is 729
Found 2 solutions by Alan3354, greenestamps:
Answer by Alan3354(69443)   (Show Source):
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
Let the first term be a; let the common ratio be r. Then the three numbers are a, ar, and ar^2.
The product of the three numbers is 729:
So we know the second number (ar) is 9.
To find the three numbers from here, we could write and solve the equation that says the sum of the three numbers is 39.
However, since both the sum and product of the three numbers are integers, we can assume the three numbers are all integers. That makes it necessary for the common ratio to be a factor of 9, so it is 1, 3, or 9; or it could be any of those integers but negative.
Of those possible common ratios, only one gives the required sum of 39: r = 3.
So r=3 and ar=9, making a=3; the three numbers are 3, 9, and 27.
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