Question 192687: find three numbers in arithmetic progression whose sum is 21 and whose product is 180?
Answer by solver91311(17077)   (Show Source):
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If the arithmetic progression has a common difference of d, and the first of the three numbers is x, then the second number must be x + d and the third, x + 2d.
So if the sum is 21, then:
 + (x + 2d) = 21)
 is the first number,
 is the second number, and
 is the third number.
Now, if the product is 180, then:
(7)(7 + d) = 180)
Rationalizing the denominator:
and the three numbers are:
 ,
 , and
 .
John
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