• Recognize the notation and terms used to represent sequences

sequence notation

A sequence is an ordered list of numbers following a specific pattern. We use special notation to represent sequences efficiently:

• [latex]a_n[/latex] represents the [latex]n[/latex]th term
• [latex]n[/latex] is the index that indicates the value’s position in the sequence.

Basic Sequence Terminology

A sequence has a few important parts:

• Terms: the individual numbers in the sequence
• Position: where each term appears in the order (1st, 2nd, 3rd, etc.)
• Index: the variable (usually [latex]n[/latex]) that represents the position

Consider the sequence: 3, 7, 11, 15, 19, …

• First term: [latex]a_1=3[/latex]
• Second term: [latex]a_2=7[/latex]
• Third term: [latex]a_3=11[/latex]

Common Sequence Notations

You’ll encounter different ways to write the same information:

Notation	Meaning
[latex]a_n[/latex]	The [latex]n[/latex]th term
[latex]{a_{n+1}[/latex]	The next term in the sequence
[latex]{a_n}_{n-1}][/latex]	The previous term in the sequence
[latex]a_1, a_2, a_3, ...[/latex]	The first term, the second term, the third term