Verified answer

1.

bₙ - арифметическая прогрессия, b₂ = -3; b₄ = 1

Воспользуемся формулой:

b₄ = b₂ + (4 - 2)·d

d = (1 - (-3)) ÷ 2

d = 2

2.

Sₙ = (b₁ + bₙ)·n / 2

S₁₄ = (b₁ + b₁₄)·14 / 2

1050 = (10 + b₁₄)·7

10 + b₁₄ = 1050 ÷ 7

b₁₄ = 140

b₁₄ = b₁ + 13d

140 = 10 + 13d

13d =  130

d = 130/13

d = 10

3.

b₂ = -5;

b₆ - b₄ = 6 ⇒ (6 - 4)d = 6; d = 3

b₁ = b₂ - d = -5 - 3 = -8

b₁₀ = b₁ + 9d = -8 + 27 = 19

S₁₀ = (b₁ + b₁₀)·10 / 2 = (-8 + 19)·5 = 55

4.

b₁ = 7; b₁₅ = 42

b₁₅ - b₁ = 14d

42 - 7 = 14d

d = 35 ÷ 14 = 2.5

b₁₂ = b₁ + 11d = 7 + 11·2.5 = 34.5 = c₁

b₂₀ = b₁ + 19d = 7 + 19·2.5 = 54.5 = c₂₀₋₁₂ = c₈

{cₙ} - арифметическая прогрессия с d = 2.5

S₈ = (c₁ + c₈)·4 = (34.5 + 54.5)·4 = 89·4 = 356 - сумма с 12-го по 24 член арифметической прогрессии {aₙ}