How is the next term in an arithmetic sequence obtained?

The next term in an arithmetic sequence is obtained by adding a constant number, known as the common difference, to the preceding term.

An arithmetic sequence, also known as an arithmetic progression, is defined by this consistent addition. Let's explore this further.

Understanding Arithmetic Sequences

An arithmetic sequence follows a pattern where the difference between consecutive terms is always the same. This difference is called the common difference.
Formula: A general formula for an arithmetic sequence is: a_n = a₁ + (n - 1)d
- a_n = nth term
- a₁ = first term
- n = term position in the sequence
- d = common difference

Let's consider an arithmetic sequence: 2, 5, 8, 11, 14...

Here's how each term is generated:

The first term is 2.
To get the second term (5), we add 3 (the common difference) to the first term (2). (2 + 3 = 5)
To get the third term (8), we add 3 to the second term (5). (5 + 3 = 8)
And so on...

To find the next term in this sequence after 14, you would simply add the common difference (3) to 14.

Therefore, the next term in the sequence would be 17.