zad 1 a₃ = a₁ + 2r = 10 a₅ = a₁ + 4r = 16 a₁ + 2r = 10 a₁ + 4r = 16 odejmujemy równania a₁ - a₁ + 2r - 4r = 10 - 16 - 2r = - 6 2r = 6 r = 6 : 2 = 3 a₁ + 2r = 10 a₁ + 2 * 3 = 10 a₁ + 6 = 10 a₁ = 10 - 6 = 4 a₁ = 4 , r = 3 a₆ = a₁ + 5 * r = 4 + 5 * 3 = 4 + 15 = 19 S₆ = (a₁ + a₆) * 6/2 = (4 + 19) * 3 = 23 * 3 = 69 zad 2 S₆ = 16 , r = - 1/2 , a₁ = ? S₆ = [2a₁ + (6 - 1) * r] * 6/2 = (2a₁ + 5r) * 3 = [2a₁ + 5 * (- 1/2)] * 3 = = (2a₁ - 5/2) * 3 = 6a₁ - 15/2 = 6a₁ - 7,5 16 = 6a₁ - 7,5 6a₁ = 16 + 7,5 = 23,5 a₁ = 23,5 : 6 = 3,91(6) zad 3 a₁₀ = a₁ + 9r = 6 a₄ = a₁ + 3r = - 2 a₁ + 9r = 6 a₁ + 3r = - 2 / * (- 3) a₁ + 9r = 6 - 3a₁ - 9r = 6 dodajemy równania a₁ - 3a₁ + 9r - 9r = 6 + 6 - 2a₁ = 12 2a₁ = - 12 a₁ = - 12 : 2 = - 6
