For example a sequence represented by the formula [tex]a_n=n^2[/tex].
[tex]a_1=1^2=1 \\
a_2=2^2=4 \\
a_3=3^2=9 \\ \\
a_2-a_1=4-1=3 \\
a_3-a_2=9-4=5 \\ \Downarrow \\ a_2-a_1 \not= a_3-a_2 \\
\hbox{not arithmetic} \\ \\
\frac{a_2}{a_1}=\frac{4}{1}=4 \\
\frac{a_3}{a_2}=\frac{9}{4}=2.25 \\ \Downarrow \\
\frac{a_2}{a_1} \not= \frac{a_3}{a_2} \\ \hbox{not geometric}[/tex]
The sequence is: 1, 4, 9, 16...
