Алгебра 9 класс учебник Макарычев, Миндюк ответы – номер 572

а) х_n = 4n + 2
x₁ = 4 · 1 + 2 = 6
x₅₀ = 4 · 50 + 2 = 202
x₂ = 4 · 2 + 2 = 10
d = x₂ – x₁ = 10 – 6 = 4

S_n = · n

S₅₀ = · 50 = 6 + 202/2 · 50 = 104 · 50 = 5200

X₁₀₀ = 4 · 100 + 2 = 402
S₁₀₀ = · 100 = 6 + 402/2 · 100 = 204 · 100 = 20400

S_n = · n = $$\frac{6 + 4_n}{2}$$ · n = (3 + 2n) · n = 3n + 2n²

Ответ: S₅₀ = 5200; S₁₀₀ = 20400; S_n = 2n² + 3n

б) x_n = 2n + 3
x₁ = 2 · 1 + 3 = 5
x₅₀ = 2 · 50 + 3 = 103
x₂ = 2 · 2 + 3 = 7
d = x₂ – x₁ = 7 – 5 = 2

S_n = · n

S₅₀ = · 50 = 5 + 103/2 · 50 = 54 · 50 = 2700

X₁₀₀ = 2 · 100 + 3 = 203

S₁₀₀ = · 100 = 5 + 203/2 · 100 = 104 · 100 = 10400

S_n = · n = $$\frac{5 + 2_n + 3}{2}$$ · n = (4 + n) · n = 4n + n²

Ответ: S₅₀ = 2700; S₁₀₀ = 10400; S_n = n² + 4n

в) x_n = n – 4
x₁ = 1 – 4 = –3
x₅₀ = 50 – 4 = 46
x₂ = 2 – 4 = –2
d = x₂ – x₁ = –2 – (–3) = 1

S_n = · n

S₅₀ = · 50 = –3 + 46/2 · 50 = 43 · 25 = 1075

X₁₀₀ = 100 – 4 = 96

S₁₀₀ = · 100 = –3 + 96/2 · 100 = 93 · 50 = 4650

S_n = · n = –3 + n – 4/2 · n = n – 7/2 · n = 0,5n² – 3,5n

Ответ: S₅₀ = 1075; S₁₀₀ = 4650; S_n = 0,5n² – 3,5n

г) x_n = 3n – 1
x₁ = 3 · 1 – 1 = 2
x₅₀ = 3 · 50 – 1 = 149
x₂ = 3 · 2 – 1 = 5
d = x₂ – x₁ = 5 – 2 = 3

S_n = · n

S₅₀ = · 50 = 2 + 149/2 · 50 = 151 · 25 = 3775

X₁₀₀ = 3 · 100 – 1 = 299

S₁₀₀ = · 100 = 2 + 299/2 · 100 = 301 · 50 = 15050

S_n = · n = $$\frac{2 + 3_n - 1}{2}$$ · n = $$\frac{3_n + 1}{2}$$ · n = 1,5n² + 0,5n

Ответ: S₅₀ = 3775; S₁₀₀ = 15050; S_n = 1,5n² + 0,5n