To find the nth term of an arithmetic sequence, you can follow a straightforward formula. An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This difference is called the ‘common difference’ and is usually denoted as ‘d’.
The formula for the nth term (often represented as an) of an arithmetic sequence can be expressed as:
an = a1 + (n – 1) * d
Where:
- a1 is the first term of the sequence.
- d is the common difference between the terms.
- n is the term number you want to find.
For example, if you have an arithmetic sequence where the first term is 2 and the common difference is 3, the sequence looks like this: 2, 5, 8, 11, …
To find the 5th term, you would plug the values into the formula:
a5 = 2 + (5 – 1) * 3
a5 = 2 + 4 * 3
a5 = 2 + 12
a5 = 14
Thus, the 5th term of the sequence is 14. This method can be used to find any term in an arithmetic sequence as long as you know the first term and the common difference.