Question

How to trun a recursive formula into a explicit formula

Answer 1

To turn a recursive formula into an explicit formula, you need to identify the base case, recurrence relation, and a pattern that connects each term to its position. For example, given a recursive sequence a_n = a_(n-1) + 5, with base case a_1 = 1, the explicit formula would be a_n = 5n - 4.

Step-by-step explanation:

Transforming a recursive formula into an explicit formula involves creating a formula that allows you to calculate the nth term directly, without needing to know any preceding terms. Here is the step-by-step process:

1. Identify the base case(s). The base case is the term(s) that starts the sequence.
2. Observe how each term is calculated from its previous term, this is the recurrence relation.
3. Try to identify a pattern, or a rule, that connects each term to its term number. This pattern will form the basis of your explicit formula.

For example, let's take a simple recursive formula a_n = a_(n-1) + 5, with a base case of a_1 = 1. After writing out several terms, we see that each term is 5 times its term number minus 4. Thus, the explicit formula is a_n = 5n - 4. This allows us to calculate the nth term directly.

Learn more about Recursive and Explicit Formulas