If there is a relationship between the elements of a sequence, the recurrence relation would be the rule that connects them. It is possible to formulate the recurrence relation and use it to find the value of each of the elements of the set according to the position it occupies.

For example

Ways to Find Recurrence Relations

There are several ways to find recurrence relations. One is to observe the sequence of elements and how they change. Another way is to write down parameters in a table.

A rule can be formulated using addition, subtraction, multiplication or division—or several of these operations together.

Let's look at an example:

Consider the sequence of elements: $3,7,11,15,19$.

If we look closely at the numbers, we can see that there is a certain rule of formation between them: to get from one number to the next, we need to add $4$ each time.

The first element is $3$. If we add $4$ to this number, we will get the second element, which is $7$. If we add $4$ to this number again, we will arrive at the third element ($11$), and so on.