[tex]a_n=6*3^n\\a_{n+1}=6*3^{n+1}\\\\\text{Z roznicy: }\\a_{n+1}-a_n=6*3^{n+1}-6*3^n=6(3^{n+1}-3^n)\\a_{n+1}-a_n=6(3^{n+1}-3^n)\\a_{n+1}=a_n+6(3^{n+1}-3^n)\\\\a_1=6*3^1=6*3=18\\\\\left \{ {{a_1=18} \atop {a_{n+1}=a_n+6(3^{n+1}-3^n)}} \right.[/tex]
[tex]\text{Z ilorazu}\\\frac{a_{n+1}}{a_n}=\frac{6*3^{n+1}}{6*3^n}=\frac{3^{n+1}}{3^n}=3^{n+1-n}=3^1=3\\\\a_{n+1}=a_n*3\\a_{n+1}=3a_n\\\\\left \{ {{a_1=18} \atop {a_{n+1}=3a_n}} \right.[/tex]
