Przyrównujemy wzór a(n) do x-a i obliczamy n, czyli numer wyrazu ciągu.
[tex]a) \ a_{n} = 5n-3 \ \ i \ \ x = 32\\\\5n-3 = 32\\\\5n = 32+3\\\\5n = 35 \ \ /:5\\\\n = 7\\\\\boxed{a_7 = x}[/tex]
[tex]b) \ a_{n} = (-2)^{n} \ \ i \ \ x = -32\\\\(-2)^{n} = -32\\\\(-2)^{n} = (-2)^{5}\\\\n = 5\\\\\boxed{a_{5} = x}[/tex]
[tex]e) \ a_{n} = \sqrt{2n-1} \ \ i \ \ x = 5\\\\\sqrt{2n-1} = 5 \ \ |^{2}}\\\\(\sqrt{2n-1})^{2} = 5^{2}\\\\2n-1 = 25\\\\2n = 25+1 \\\\2n = 26 \ \ /:2\\\\n = 13\\\\\boxed{a_{13} = x}[/tex]
[tex]f) \ a_{n} = n(n^{2}-3n+2) \ \ i \ \ x = 6\\\\n(n^{2}-3n+2) = 6\\\\n^{3}-3n^{2}+2n-6 = 0\\\\n^{2}(n-3)+2(n-3) = 0\\\\(n-3)(n^{2}+2) = 0\\\\n-3 = 0 \ \vee \ n^{2}+2 = 0\\\\n = 3 \ \vee \ n^{2}\neq -2\\\\n = 3\\\\\boxed{a_{3} = x}[/tex]
