Index variable

Definition

An index variable is a variable that represents the position of an element in a sequence or series. It is typically denoted by symbols such as $n$, $i$, or $k$.

5 Must Know Facts For Your Next Test

1. The index variable often starts from 1 or 0, depending on the context.
2. In mathematical notation, it is usually written as a subscript, e.g., $a_n$ for the nth term in a sequence.
3. The value of the index variable increments with each subsequent term in the sequence.
4. It helps to define recursive relationships where each term depends on previous terms.
5. Index variables are crucial for expressing sums and products in series, such as $\sum_{i=1}^n a_i$.

Review Questions

• What symbol is commonly used to denote an index variable?
• How does an index variable help in defining sequences and series?
• Explain how an index variable functions in the summation notation.

Related terms

Sequence: An ordered list of numbers following a particular pattern or rule.

Series: The sum of the terms of a sequence.

$\sum$ (Summation Notation): A mathematical notation used to represent the sum of a sequence of terms, using an index variable.