Szczegółowe wyjaśnienie:
O ciągu arytmetycznym wiemy, że mając wyrazy: a, b, c
To [tex]b=\frac{a+c}{2}[/tex]
x+1; 4x-1; 3x+5
[tex]4x-1=\frac{x+1-(3x+5)}{2}[/tex]
[tex]4x-1=\frac{x+1-3x-5}{2}[/tex]
[tex]4x-1=\frac{-2x-4}{2}[/tex]
[tex]4x-1=-x-2[/tex]
[tex]5x=-1[/tex]
[tex]x=-\frac{1}{5}[/tex]
[tex]a_{1} =x+1=-\frac{1}{5} +1=-\frac{4}{5}[/tex]
[tex]a_{2} =4x-1=4*(-\frac{1}{5} )-1=-\frac{4}{5} -1=-1\frac{4}{5}[/tex]
[tex]r=a_{2}-a_{1} =-1\frac{4}{5} -(-\frac{4}{5} )=-1\frac{4}{5} +\frac{4}{5}=-1[/tex]
[tex]a_{n} =a_{1}+(n-1)r[/tex]
[tex]a_{n} =-\frac{4}{5} +(n-1)(-1)[/tex]
[tex]a_{n} =-\frac{4}{5} -n+1[/tex]
[tex]a_{n} =-n+\frac{1}{5}[/tex]
