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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
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- ALGEBRA-II - YOUR ONLINE TEXTBOOK.
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