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english Prove that if 1/(a+b), 1/(a+c) and 1/(b+c) are the consecutive terms of an arithmetic sequence, then a2, b2 and c2 are also in arithmetic progression (and vice versa).
francais Démontrez que si 1/(a+b), 1/(a+c) et 1/(b+c) sont les termes d’un séquence arithmétique, alors a2, b2 et c2 sont eux aussi en progression arithmétique (et réciproquement).
italiano Dimostrare che se 1/(a+b), 1/(a+c) e 1/(b+c) sono i termini consecutivi di una successione aritmetica, allora a2, b2 e c2 sono anch’essi in progressione aritmetica (e viceversa).

Sunday puzzle 55

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Text and images by Gianni A. Sarcone 
Labels: SUNDAY PUZZLE, puzzles to solve, recreational mathematics, progression
You can use the material shown on this page for educational purpose only as long as you credit us [© G. Sarcone,] and link back to
Creative Commons LicenseSunday Puzzle by Gianni A. Sarcone is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
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