[latex]a)a_n = (2k-3)n-6 = 2kn-3n-6\a_{n+1} = (2k-3)(n+1)-6 = 2kn+2k-3n-3\\a_{n+1}-a_n =2kn+2k-3n-3-(2kn-3n-6) =2k+3\\Ciag jest rosnacy gdy a_{n+1}-a_n >0.\\2k+3>0 \2k>-3\k> -frac32[/latex] [latex]b) a_n = (k^2-1)n+4 = k^2n-n+4\\a_{n+1} = (k^2-1)(n+1)+4 = k^2n+k^2-n-1+4 = k^2n+k^2-n+3\\a_{n+1}-a_n = k^2n+k^2-n+3 -k^2n+n-4 = k^2-1\\k^2-1>0\\(k-1)(k+1)>0\\k_1 = 1 ; k_2 = -1\\k in (-infty;-1) cup (1; infty)[/latex] [latex]c) a_n = (3-k^2)n = 3n - k^2n\\a_{n+1} = (3-k^2)(n+1) = 3n+3-k^2n-k^2\\a_{n+1}-a_n = 3n+3-k^2n-k^2-3n+k^2n = 3-k^2\\\3-k^2>0\\(sqrt3-k)(sqrt3+k)>0\\k_1 = sqrt3 ; k_2 = -sqrt3\\k in (-sqrt3; sqrt3)[/latex]
