Решение
a₂ = a₁ + d
a₉ =a₁ + 8d
a₂ = 3a₉
3(a₁ + 8d) = a₁ + d
3a₁ + 24d = a₁ + d
2a₁ + 23d = 0
2a₁ = - 23d
a₁ = - 11,5d
Sn = [2a₁ + d*(n - 1)*n]/2
S₂₀ = [(a₁ + a₁ + 19d)*20]/2 = (a₁ + a₂₀)*10
S₂₀ = (2a₁ + 19d)*10 = [2*(-11,5d) + 19d]*10 = (-23d + 19d)*10 = -4d*10 = - 40d
S₂₀ = - 40d
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Verified answer
Решение
a₂ = a₁ + d
a₉ =a₁ + 8d
a₂ = 3a₉
3(a₁ + 8d) = a₁ + d
3a₁ + 24d = a₁ + d
2a₁ + 23d = 0
2a₁ = - 23d
a₁ = - 11,5d
Sn = [2a₁ + d*(n - 1)*n]/2
S₂₀ = [(a₁ + a₁ + 19d)*20]/2 = (a₁ + a₂₀)*10
S₂₀ = (2a₁ + 19d)*10 = [2*(-11,5d) + 19d]*10 = (-23d + 19d)*10 = -4d*10 = - 40d
S₂₀ = - 40d