- Arithmetic sequence - Glossary Term
An arithmetic sequence is a sequence of numbers such that the difference between any two successive members of the sequence is constant.
For example, the sequence
2, 5, 8, 11, 14, 17, …
is an arithmetic sequence with first term 2 and common difference 3.
By inspection of the sequence, the rule for the nth term tn of this sequence is:
tn = 2 + (n – 1)3 = 3n –1 n ≥ 1
If tn is used to denote the nth term in the sequence, then a recursion relation that will generate this sequence is: t1 = 2, tn +1 = tn + 3 n ≥ 1