[tex]a_n=n^2+3n-31\\a_{n+1}=(n+1)^2+3(n+1)-31=n^2+2n+1+3n+3-31=n^2+5n-27[/tex]
[tex]a_{n+1}-a_n=r[/tex]
[tex]r=n^2+5n-27-(n^2+3n-31)\\r=n^2+5n-27-n^2-3n+31\\r=2n+4\\\\\text{Dla ciagu rosnacego }r > 0\\\\r > 0\\2n+4 > 0\\2n > -4 /:2\\n > -2\\\\\text{Dla ciagu malejacego } r < 0\\r < 0\\2n+4 < 0 /-4\\2n < -4 /:2\\n < -2\\[/tex]
