- Geometric sequence - Glossary Term
A geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed non-zero number called the common ratio. For example, the sequence
2, 6, 18, ...
is a geometric sequence with first term 2 and common ratio 3.
By inspection of the sequence, the rule for the nth term of this sequence is:
tn = 2 × 3n – 1n ≥ 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 = 3tn n ≥ 1