# Archimedes Laboratory Project™ Puzzles & Mental Activities that Enhance Critical and Creative Thinking Skills

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SUNDAY PUZZLE #55
 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). 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). 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). You can comment and discuss this puzzle on our FaceBook or Blogger web page. › Click to show/hide the solution

Text and images by Gianni A. Sarcone
Labels: SUNDAY PUZZLE, puzzles to solve, recreational mathematics, progression
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