Arithmetic Sequences
What is an arithmetic sequence?
- In an arithmetic sequence, the difference between consecutive terms in the sequence is constant
- This means a common difference is added to each term to get the next term
- The first term of the sequence is denoted by
- The common difference is denoted by
- For example, 1, 4, 7, 10, … is an arithmetic sequence with the rule ‘start at one and add three to each number’
- The first term, , is 1
- The common difference, , is 3
- For example, 1, 4, 7, 10, … is an arithmetic sequence with the rule ‘start at one and add three to each number’
- An arithmetic sequence can be
- increasing (positive common difference), or
- decreasing (negative common difference)
- Terms in an arithmetic sequence can be referred to
- by the letter with
- a subscript corresponding to its place in the sequence
- e.g. is the first term, is the ninth term, is the th term, etc.