Arithmetic Sequence Recursive Formula

About Arithmetic Sequence Recursive Formula

Let us review what an arithmetic sequence is before learning the recursive formula for an arithmetic series. It's a number sequence in which each succeeding term is obtained by adding a specified number to the term before it. For example, the arithmetic sequence -1, 1, 3, 5,... is formed by adding a fixed integer 2 to the previous term. The common difference is commonly indicated by d, and it is a fixed integer. Let's look at the recursive arithmetic sequence formula and some solved examples

What Is Arithmetic Sequence Recursive Formula?

In the case of an arithmetic sequence, recursion is the process of discovering one of its terms by applying fixed logic to the previous term. Every term of an arithmetic series is obtained by adding a fixed integer (known as the common difference, d) to its previous term, as we learned in the previous section. As a result, the recursive arithmetic sequence formula is:

The n^th term of an arithmetic Sequence a₁,a₂,a₃,.......,a_n....... is

a_n = a_n-1 + d, Where

a_n = the n ^th term
a_{n-1 = the (n - 1) ^th term}
d = Common differece

= a₂ - a₁(or)a₃ - a₂=....... = a_n-a_n-1