Odpowiedź:
6 wyrazów
Szczegółowe wyjaśnienie:
[tex]a_{n} = n^{2}-2n\\\\n^{2}-2n < 35\\\\\\n^{2}-2n-35 = 0\\\\a = 1, \ b = -2, \ c = -35\\\\\Delta = b^{2}-4ac = (-2)^{2}-4\cdot1\cdot(-35) = 4 + 140 = 144\\\\\sqrt{\Delta} = \sqrt{144} = 12\\\\n \in \ N^{+}\\\\n_1 = \frac{-b-\sqrt{\Delta}}{2a} = \frac{2-12}{2} = \frac{-10}{2} = -5 \ \ \ \not\in D\\\\n_2 = \frac{-b+\sqrt{\Delta}}{2a} = \frac{2+12}{2} = \frac{14}{2} = 7\\\\a > 0, \ to \ ramiona \ wykresu \ paraboli \ skierowane \ do \ gory\\\\n \in (0;7)\\\\n \in \{1,6\}\\\\\boxed{n = 6}[/tex]
LUB
[tex]a_{n} = n^{2}-2n[/tex]
[tex]a_1 = 1^{2}-2\cdot1 = 1-2 = -1 < 35\\\\a_2 = 2^{2}-2\cdot2 = 4 - 4 = 0 < 35\\\\a_3 = 3^{2}-2\cdot3 = 9-6 = 3 < 35\\\\a_4 = 4^{2} -2\cdot4 = 16 - 8 = 8 < 35\\\\a_5 = 5^{2}-2\cdot5=25 - 10=15 < 35\\\\a_6 = 6^2- 2\cdot 6=36-12 =24 < 36\\-----------------\\\\a_7= 7^{2}-2\cdot7 = 49-14 = 35[/tex]
