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 nth term of an arithmetic Sequence a1,a2,a3,.......,an....... is
an = an-1 + d, Where
- an = the n th term
- an-1 = the (n - 1) th term
-
d = Common differece
= a2 - a1(or)a3 - a2=....... = an-an-1
Arithmetic Sequence Recursive Formula
The arithmetic sequence recursive formula is:
an=an−1+d
where,
- an = nth term of the arithmetic sequence.
- an−1 = (n - 1)th term of the arithmetic sequence (which is the previous term of the nth term).
- d = The common difference (the difference between every term and its previous term).
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