579. Найдите десятый и п-й члены арифметической прогрессии: a) ⅓; -1;...; 6) 2,3; 1; . .

Решение:

a) ⅓; -1; ...

• a₁ = ⅓
• d = -1 - ⅓ = -\(\frac{3}{3}\) - \(\frac{1}{3}\) = -\(\frac{4}{3}\)
• a₁₀ = a₁ + (10 - 1) * d = \(\frac{1}{3}\) + 9 * (- \(\frac{4}{3}\)) = \(\frac{1}{3}\) - \(\frac{36}{3}\) = -\(\frac{35}{3}\) = -11 \(\frac{2}{3}\)
• aₙ = a₁ + (n - 1) * d = \(\frac{1}{3}\) + (n - 1) * (- \(\frac{4}{3}\)) = \(\frac{1}{3}\) - \(\frac{4}{3}\)(n - 1)

б) 2,3; 1; ...

• a₁ = 2,3
• d = 1 - 2,3 = -1,3
• a₁₀ = a₁ + (10 - 1) * d = 2,3 + 9 * (-1,3) = 2,3 - 11,7 = -9,4
• aₙ = a₁ + (n - 1) * d = 2,3 + (n - 1) * (-1,3) = 2,3 - 1,3(n - 1)