##A sequence is a function $a:A\to B$ where $A \subseteq \m Z$ (usually $A = \m N$ or $A = \m N-\{0\}$)<br> #The $n^{\mbox{th}}$ term is $a_n=a(n)$ <br> #An arithmetic sequence is of the form $a_n=bn+c$ <br> #A geometric sequence is of the form $a_n=br^n$ <br> ##<b>Growth of functions:</b><br> #$f(x)$ is $O(g(x))$ means $\exists k,C\ \forall x\ (x>k \to |f(x)|\le C|g(x)|)$ <br> #$f(x)$ is $\Omega(g(x))$ means $\exists k,C>0\ \forall x\ (x>k \to |f(x)|\ge C|g(x)|)$ <br> #$f(x)$ is $\Theta(g(x))$ means $f(x)$ is $O(g(x))$ and $f(x)$ is $\Omega(g(x))$ <br> #$f(x)$ is $\Theta(g(x))$ is equivalent to $\exists k,C,D>0\ \forall x\ (x>k \to D|g(x)|\le |f(x)|\le C|g(x)|)$ <br>