Question

Найти первый член и разность арифметической прогрессии (Аn) если: А2 + А6 = 24 и А2 * А3 = 54

Answer 1

A₂ + a₆ = 24                                    a₂ * a₃ = 54
a₁ + d + a₁ + 5d = 24                     ( a₁ + d) * (a₁ + 2d) = 54
2a₁ + 6d = 24
a₁ + 3d = 12
a₁ = 12 - 3d
(12 - 3d + d)(12 - 3d + 2d ) = 54
(12 - 2d)(12 - d) = 54
144 - 12d - 24d + 2d² = 54
2d² - 36d + 90 = 0
d² - 18d + 45 = 0
 d₁ = 3       d₂ = 15
a₁ = 12 - 3*3 = 12 - 9 = 3
a₂= 12 - 3 * 15 = 12 - 45 = - 33