Series

• Arithmetic nth term

  $u_n=$ $a+$$\left(n-1\right)d$
• Arithmetic sum

  $S_n=$ $\frac{n}{2}\left(2a\ +\left(n-1\right)d\right)$

  $S_n=$ $\frac{n}{2}\left(a\ +\ L\right)$ where a is the first term and L is the last term
• Geometric nth term

  $u_n=$ $ar^{n-1}$
• Geometric sums

  $S_n=$ $\frac{a\left(1-r^n\right)}{1-r}$

  $S_{\infty}=$ $\frac{a}{1-r}$
• It's an increasing sequence if $u_{n+1}>u_n$ for all n
• It's a decreasing sequence if $u_{n+1}<u_n$ for all n
• It's a period sequence if $u_{n+k}=$$u_n$ for all n and its period/order is k