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

Algebra ->  Sequences-and-series -> SOLUTION: three consecutive terms if an AP have sum 21 and product 315.find the three numbers of the arithmetic progression.       Log On


   

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) About Me  (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
x%2814+-+x%29=+45
x%5E2+-14x+%2B+45+=+0
%28x+-+5%29%28x+-+9%29+=+0
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.