Recursive Rule Calculator

Formula

To calculate the next term in a sequence using a recursive rule:

\[ a_n = a_{n-1} + d \]

Where:

\(a_n\) is the nth term in the sequence
\(a_{n-1}\) is the previous term in the sequence
\(d\) is the common difference between the terms

What is a Recursive Rule?

A recursive rule is a mathematical rule or formula that uses the output of one step to determine the output of the next step. It is a way of defining a sequence or a pattern of numbers where each term is a function of the preceding term. This rule is often used in computer programming and mathematics, particularly in algorithms and functions, to solve complex problems by breaking them down into simpler, repetitive steps.

Example Calculation 1

Let's assume the following values:

Previous Term (\(a_{n-1}\)) = 5
Common Difference (\(d\)) = 3

Use the formula:

\[ a_n = 5 + 3 = 8 \]

The next term (\(a_n\)) is 8.

Example Calculation 2

Let's assume the following values:

Previous Term (\(a_{n-1}\)) = 10
Common Difference (\(d\)) = -2

Use the formula:

\[ a_n = 10 + (-2) = 8 \]

The next term (\(a_n\)) is 8.