What is an arithmetic sequence?
An arithmetic sequence is a sequence where the difference between one term and the previous term is always the same. So the difference between the 1st and the 2nd term is the same as the difference between the 10th and 11th term. This can be described recursively as or explicitly as:
Example of an arithmetic sequence
Consider the following sequence:
We can find the difference by subtracting two terms: . And indeed the difference between every term is 3. Now, to express this sequence explicitly in the general form given above:
So to find the 5th element, for example, we get . We see that this is the same as the 5th element in the sequence above.