Explicit formulas

Definition

An explicit formula directly defines the $n$-th term of a sequence as a function of $n$. It allows for the calculation of any term without needing previous terms.

5 Must Know Facts For Your Next Test

1. Explicit formulas are often simpler to work with than recursive formulas.
2. They can be used to find any term in a sequence directly, based on its position.
3. Common forms include polynomial, exponential, and trigonometric functions.
4. The general form is given by $a_n = f(n)$ where $f(n)$ is a specific function.
5. In contrast to explicit formulas, recursive formulas require the computation of prior terms.

Review Questions

Related terms

Sequence:

An ordered list of numbers following some rule or pattern.

Recursive Formula: Defines each term of a sequence using preceding terms.

Arithmetic Sequence:

A sequence where each term is obtained by adding a constant difference to the previous term.