Zada). a1 = 9, q = 2, an = 1152 n = ? Korzystam ze wzoru na n-ty wyraz ciagu geometrycznego an = a1*q(do potegi n-1) an= 9*2(do potegi n-1) = 1152 9*2(do potegi n-1) = 1152 /:9 2(do potegi n-1) = 128 2 (do potegi n): 2 = 128 /*2 2( do potegi n) = 256 2( do potegi n) = 2⁸ n = 8 Zad.b) a1 = 25 q = -3 an = 2025 n = ? Korzystam ze wzoru na n-ty wyraz ciagu geometrycznego an = a1*q(do potegi n-1) an= 25*(-3)(do potegi n-1) = 2025 25*(-3)(do potegi n-1) = 2025 /:25 (-3)(do potegi n-1) = 81 (-3) do potegi n : (-3) = 81 /*(-3) (-3) do potegi n = -243 (-3) do potegi n = (-3)⁵ n = 5 Zadc) a1 = 54 q = 1/3 an = 2/243 n = ? Korzystam ze wzoru na n-ty wyraz ciagu geometrycznego an = a1*q(do potegi n-1) an= 54*(1/3)(do potegi n-1) = 2/243 54*(1/3)(do potegi n-1) = 2/243 /:54 (1/3)(do potegi n-1) = 1/6561 (1/3) do potegi n : (1/3) = 1/6561 [(1/3) do potegi n ] *3 = 1/6561 /*1/3 (1/3)do potegi n = 1/19683 (1/3) do potegi n = (1/3)⁹ n = 9
