3. Найдите второй, пятый и десятый члены последовательности (хₙ), заданной формулой: a) xₙ = n + 6; б) xₙ = (2n-1)/3; в) xₙ = n²; г) xₙ = n (n - 1); д) xₙ = n³ - n; е) xₙ = (-1)ⁿ · n.

a) xₙ = n + 6;

1. n = 2: $$x₂ = 2 + 6 = 8$$
2. n = 5: $$x₅ = 5 + 6 = 11$$
3. n = 10: $$x₁₀ = 10 + 6 = 16$$

Ответ: 8, 11, 16

б) xₙ = (2n-1)/3;

1. n = 2: $$x₂ = (2 \cdot 2 - 1)/3 = (4 - 1)/3 = 3/3 = 1$$
2. n = 5: $$x₅ = (2 \cdot 5 - 1)/3 = (10 - 1)/3 = 9/3 = 3$$
3. n = 10: $$x₁₀ = (2 \cdot 10 - 1)/3 = (20 - 1)/3 = 19/3$$

Ответ: 1, 3, 19/3

в) xₙ = n²;

1. n = 2: $$x₂ = 2² = 4$$
2. n = 5: $$x₅ = 5² = 25$$
3. n = 10: $$x₁₀ = 10² = 100$$

Ответ: 4, 25, 100

г) xₙ = n (n - 1);

1. n = 2: $$x₂ = 2 \cdot (2 - 1) = 2 \cdot 1 = 2$$
2. n = 5: $$x₅ = 5 \cdot (5 - 1) = 5 \cdot 4 = 20$$
3. n = 10: $$x₁₀ = 10 \cdot (10 - 1) = 10 \cdot 9 = 90$$

Ответ: 2, 20, 90

д) xₙ = n³ - n;

1. n = 2: $$x₂ = 2³ - 2 = 8 - 2 = 6$$
2. n = 5: $$x₅ = 5³ - 5 = 125 - 5 = 120$$
3. n = 10: $$x₁₀ = 10³ - 10 = 1000 - 10 = 990$$

Ответ: 6, 120, 990

е) xₙ = (-1)ⁿ · n.

1. n = 2: $$x₂ = (-1)² \cdot 2 = 1 \cdot 2 = 2$$
2. n = 5: $$x₅ = (-1)⁵ \cdot 5 = -1 \cdot 5 = -5$$
3. n = 10: $$x₁₀ = (-1)^{10} \cdot 10 = 1 \cdot 10 = 10$$

Ответ: 2, -5, 10