A sequence of numbers arranged according to a rule is called a sequence. The nth number is written as a_n, and the entire sequence is written as {a_n}.
A sequence in which the difference between consecutive terms is constant is called an arithmetic sequence, and this difference d is called the common difference.
a_{n+1} − a_n = d (constant)
Example ① Is 3, 7, 11, 15, … an arithmetic sequence? What is its common difference?
Solution: Since the difference is always 4, it is an arithmetic sequence. Common difference d = 4
Solution: Since the difference is always 4, it is an arithmetic sequence. Common difference d = 4
Key Point
- Arithmetic sequence ⇔ the difference between consecutive terms is constant
- The common difference can be positive, negative, or 0
Practice Problems
- The common difference of 10, 7, 4, 1, …
Answer and Explanation
- Answer: −3