'bjour...
u₁ + u₂ + u₃ = u₁ + u₁ + R + u₁ + 2R = 3(u₁ + R)
==> 3(u₁ + R) = 15 ==> u₁ + R = 5
u₂² = u₁² + 2Ru₁ + R²
u₃² = u₂² + 2Ru₂ + R² = u₁² + 4Ru₁ + 4R²
==> u₁² + u₂² + u₃² = 3u₁² + 6Ru₁ + 5R²
= 3(u₁ + R)² - 3R² + 5R²
= 3 x 25 + 2R²
==> 2R² + 75 = 83
==> R² = 4
==> R = 2 (R > 0 car (Un) croissante)
Et donc u₁ = 5 - R = 3
u₂ = 5 et u₃ = 7
On vérifie :
3 + 5 + 7 = 15
3² + 5² + 7² = 9 + 25 + 49 = 83
