[tex]a_1 = x+1\\a_2 = 4x-1\\a_3 = 3x+5\\a_{n} = ?[/tex]
Z własności ciągu arytmetycznego:
[tex]a_2 = \frac{a_1+a_3}{2}\\\\4x-1 = \frac{x+1+3x+5}{2}\\\\4x-1=\frac{4x+6}{2}\\\\4x-1 = 2x+3\\\\4x-2x=3+1\\\\2x=4 \ \ /:2\\\\\underline{x = 2}\\\\Zatem:\\a_1 = 2+1 = 3\\a_2 = 4\cdot2 = 8-1 = 7\\r = a_2-a_1 = 7-3 = 4\\\\\\a_{n} = a_1 + (n-1)\cdot r\\\\a_{n} = 3+(n-1)\cdot4\\\\a_{n} = 3+4n-4\\\\\boxed{a_{n} = 4n-1}[/tex]
