672. Вычислите первые несколько членов последовательности (ул), если: а) У₁ = -3, Yn+1 - Yn = 10; б) У₁ = 10, Уn + 1 * Yn = 2,5; в) У₁ = 1,5, Yn + 1 - Yn = n; г) У₁ = −4, Уп +1: Yn = -n².

а) \( y_1 = -3, \quad y_{n+1} - y_n = 10 \)

1. \( y_1 = -3 \)
2. \( y_2 = y_1 + 10 = -3 + 10 = 7 \)
3. \( y_3 = y_2 + 10 = 7 + 10 = 17 \)
4. \( y_4 = y_3 + 10 = 17 + 10 = 27 \)
5. \( y_5 = y_4 + 10 = 27 + 10 = 37 \)

б) \( y_1 = 10, \quad y_{n+1} \cdot y_n = 2.5 \)

1. \( y_1 = 10 \)
2. \( y_2 = \frac{2.5}{y_1} = \frac{2.5}{10} = 0.25 \)
3. \( y_3 = \frac{2.5}{y_2} = \frac{2.5}{0.25} = 10 \)
4. \( y_4 = \frac{2.5}{y_3} = \frac{2.5}{10} = 0.25 \)
5. \( y_5 = \frac{2.5}{y_4} = \frac{2.5}{0.25} = 10 \)

в) \( y_1 = 1.5, \quad y_{n+1} - y_n = n \)

1. \( y_1 = 1.5 \)
2. \( y_2 = y_1 + 1 = 1.5 + 1 = 2.5 \)
3. \( y_3 = y_2 + 2 = 2.5 + 2 = 4.5 \)
4. \( y_4 = y_3 + 3 = 4.5 + 3 = 7.5 \)
5. \( y_5 = y_4 + 4 = 7.5 + 4 = 11.5 \)

г) \( y_1 = -4, \quad \frac{y_{n+1}}{y_n} = -n^2 \)

1. \( y_1 = -4 \)
2. \( y_2 = y_1 \cdot (-1^2) = -4 \cdot (-1) = 4 \)
3. \( y_3 = y_2 \cdot (-2^2) = 4 \cdot (-4) = -16 \)
4. \( y_4 = y_3 \cdot (-3^2) = -16 \cdot (-9) = 144 \)
5. \( y_5 = y_4 \cdot (-4^2) = 144 \cdot (-16) = -2304 \)