zad 1 [latex]a_{n}=-n^{2}+13n+14\ a_{n} extless 0\ -n^{2}+13n+14 extless 0\ \ Delta=b^{2}-4ac\ Delta=13^{2}-4*(-1)*14\ Delta=169+56\ Delta=225\ sqrt{Delta}=15\ \ n_{1}=frac{-b-sqrt{Delta}}{2a}=frac{-13-15}{-2}=frac{-28}{-2}=14\ \ n_{2}=frac{-b+sqrt{Delta}}{2a}=frac{-13+15}{-2}=frac{2}{-2}=-1[/latex] ---> a=-1<0 - parabola skierowana ramionami w górę, stąd: an < 0 dla n∈(-∞, -1) u (14, ∞) ale: n∈N, czyli: Odp. an < 0 dla n∈ N ∧ n∈(14, ∞) [n∈{15, 16, 17, 18, ... } zad 2 [latex]a_{n-1}=4x-10\ a_{n}=4x-8\ a_{n+1}=3x-8\ \ a_{n+1}-a_{n}=a_{n}-a_{n-1}\ 3x-8-(4x-8)=4x-8-(4x-10)\ 3x-8-4x+8=4x-8-4x+10\ -x=2 |*(-1)\ x=-2[/latex]
1. Nie wiem [latex]2.\ frac{a_{n-1}+a_{n}+a_{n+1}}{3} =a_n\ frac{4x-10+4x-8+3x-8 }{3}=4x-8|*3\ 11x-26=12x-24\ x=-2[/latex]
