Задание 37. Заполните таблицу. 1) 3 5 5-3=2 7 a₇ =3+2.(7-1)= 3+12=15 2) 4 7 5 3) 2 -2 8 4) -1 5 10 5) -10 -5 6 6) 12 5 14 7) 15 3 22 8) 11 7 16 9) -12 -3 27 10) 0,4 1,1 11

Решим задачу, заполнив таблицу, где требуется найти значения d, n и aₙ для арифметической прогрессии.

1. Дано: a₁ = 3, a₂ = 5, d = 5 - 3 = 2, n = 7

   a₇ = 3 + 2 × (7 - 1) = 3 + 2 × 6 = 3 + 12 = 15

2. Дано: a₁ = 4, a₂ = 7, d = a₂ - a₁ = 7 - 4 = 3, n = 5

   a₅ = a₁ + d × (n - 1) = 4 + 3 × (5 - 1) = 4 + 3 × 4 = 4 + 12 = 16

3. Дано: a₁ = 2, a₂ = -2, d = a₂ - a₁ = -2 - 2 = -4, n = 8

   a₈ = a₁ + d × (n - 1) = 2 + (-4) × (8 - 1) = 2 + (-4) × 7 = 2 - 28 = -26

4. Дано: a₁ = -1, a₂ = 5, d = a₂ - a₁ = 5 - (-1) = 6, n = 10

   a₁₀ = a₁ + d × (n - 1) = -1 + 6 × (10 - 1) = -1 + 6 × 9 = -1 + 54 = 53

5. Дано: a₁ = -10, a₂ = -5, d = a₂ - a₁ = -5 - (-10) = 5, n = 6

   a₆ = a₁ + d × (n - 1) = -10 + 5 × (6 - 1) = -10 + 5 × 5 = -10 + 25 = 15

6. Дано: a₁ = 12, d = 5, n = 14

   a₂ = a₁ + d = 12 + 5 = 17

   a₁₄ = a₁ + d × (n - 1) = 12 + 5 × (14 - 1) = 12 + 5 × 13 = 12 + 65 = 77

7. Дано: a₁ = 15, d = 3, n = 22

   a₂ = a₁ + d = 15 + 3 = 18

   a₂₂ = a₁ + d × (n - 1) = 15 + 3 × (22 - 1) = 15 + 3 × 21 = 15 + 63 = 78

8. Дано: a₂ = 11, d = 7, n = 16

   a₁ = a₂ - d = 11 - 7 = 4

   a₁₆ = a₁ + d × (n - 1) = 4 + 7 × (16 - 1) = 4 + 7 × 15 = 4 + 105 = 109

9. Дано: a₂ = -12, d = -3, n = 27

   a₁ = a₂ - d = -12 - (-3) = -9

   a₂₇ = a₁ + d × (n - 1) = -9 + (-3) × (27 - 1) = -9 + (-3) × 26 = -9 - 78 = -87

10. Дано: a₁ = 0.4, a₂ = 1.1, d = a₂ - a₁ = 1.1 - 0.4 = 0.7, n = 11

    a₁₁ = a₁ + d × (n - 1) = 0.4 + 0.7 × (11 - 1) = 0.4 + 0.7 × 10 = 0.4 + 7 = 7.4

Заполненная таблица:

Ответ: смотри таблицу выше.