- listing all terms of a finite sequence:

$2, 5, 8, 11, 14, 17$ - listing the first few terms and assuming that the pattern represented continuous indefinitely:

$2, 5, 8, \cdots $ - giving a description in words:

$\textit{Starts at 2, and each term is 3 more than the previous term}$ - using a formula which represents the general term of $n$th term:

$u_{n}=3n-1$

A pentagon is made using matches.

By adding more matches, a row of two pentagons is formed.

Continuing to add matches, a row of three pentagons can be formed.

If $u_{n}$ represents the number of matches in $n$ pentagons, then $u_{1}=5,u_{2}=9,u_{3}=13$ and so on.

This sequence can be specified by:

- listing terms:

$5, 9, 13, \cdots$ - using words:

$\textit{The first term is 5 and each term is 4 more than the previous term.}$ - using an explicit formula:

$u_{n}=4n+1$

## General Term

The $\textit{General Term}$ or $n$th term of a sequence is represented by a symbol with a subscript.For example, $u_{n}$, $T_{n}$ or $A_{n}$. The general term is defined for $n=1,2,3,4, \cdots$.

$\{u_{n}\}$ represents the sequence that can be generated by using $u_{n}$ as the $n$th term.

For example, $\{3n-1\}$ generates the sequence:

\( \begin{align} \displaystyle u_{1} &= 3 \times 1 - 1 = 2 \\ u_{2} &= 3 \times 2 - 1 = 5 \\ u_{3} &= 3 \times 3 - 1 = 8 \\ \end{align} \)