Question 1117935: Three numbers are in arithmetic progression,their sum is15and their product is 80.Determine the numbers
Answer by ikleyn(52798)   (Show Source):
You can put this solution on YOUR website! .
Let "x" be the second term of the AP, and let "d" be its common difference.
Then the terms are a-d, a and a+d.
The sum of the three terms is 15, which gives you an equation 3a = 15, or a =  = 5.
Next equation, from the condition, is
(5-d)*5*(5+d) = 80, or 25 - d^2 = 16 ====> d^2 = 25 - 16 = 9 ====> d = +/- 3.
Thus there are two arithmetic progressions satisfying the condition.
First AP is 5-3, 5, 5+3, or 2, 5, 8.
The second AP is 5+3, 5, 5-3, or 8, 5, 2.
Solved.
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There is a bunch of lessons on arithmetic progressions in this site:
- Arithmetic progressions
- The proofs of the formulas for arithmetic progressions
- Problems on arithmetic progressions
- Word problems on arithmetic progressions
- Mathematical induction and arithmetic progressions
- One characteristic property of arithmetic progressions
- Solved problems on arithmetic progressions
Also, you have this free of charge online textbook in ALGEBRA-II in this site
- ALGEBRA-II - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this online textbook under the topic "Arithmetic progressions".
Save the link to this textbook together with its description
Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson
into your archive and use when it is needed.
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