191. Найдите формулу n-го члена арифметической прогрессии: 1) 18, 14, 10, 6, ... ; 2) b₁ = -1/27, 2/3, bₙ, 2²/3, ... ; 3) a⁴, 5a⁴, 9a⁴, 13a⁴, ... ; 4) 10-a, 8-а, 6-а, 4-а, ... .

Решение:

1. 18, 14, 10, 6, ...
   d = 14 - 18 = -4
   aₙ = 18 + (n - 1)(-4) = 18 - 4n + 4 = 22 - 4n
2. b₁ = -1/27, 2/3, bₙ, 2²/3, ...
   Преобразуем члены прогрессии: b₁ = -1/27, b₂ = 2/3 = 18/27, b₃ = 12/3 = 36/27
   d = 18/27 - (-1/27) = 19/27
   bₙ = -1/27 + (n - 1)(19/27) = -1/27 + (19n - 19)/27 = (19n - 20)/27
3. a⁴, 5a⁴, 9a⁴, 13a⁴, ...
   d = 5a⁴ - a⁴ = 4a⁴
   aₙ = a⁴ + (n - 1)(4a⁴) = a⁴ + 4na⁴ - 4a⁴ = 4na⁴ - 3a⁴
4. 10-a, 8-а, 6-а, 4-а, ...
   d = (8 - a) - (10 - a) = -2
   aₙ = (10 - a) + (n - 1)(-2) = 10 - a - 2n + 2 = 12 - a - 2n

Ответ: 1) aₙ = 22 - 4n; 2) bₙ = (19n - 20)/27; 3) aₙ = 4na⁴ - 3a⁴; 4) aₙ = 12 - a - 2n