SOLUTION: three consecutive terms if an AP have sum 21 and product 315.find the three numbers of the arithmetic progression.

Question 637907: three consecutive terms if an AP have sum 21 and product 315.find the three numbers of the arithmetic progression.

Answer by reviewermath(1029) (Show Source): You can put this solution on YOUR website!
Let x be the first term and k be the common difference.
The three consecutive terms of the sequence are x, x + k, and x + 2k.
sum: 3x + 3k = 21 or x + k = 7 or k = 7 - x
product: x(x + k)(x + 2k) = 315, substitute k = 7 - x
x(7)(14 - x) = 315, divide both sides by 7

If x = 5, then k =2 and the terms of the sequence are 5, 7, and 9.
If x = 9 then k = -2 and the terms of the sequence are 9, 7, and 5.
Answer: 5, 7, and 9.

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