Summary: Geometric Sequences

Key Equations

recursive formula for nth term of a geometric sequence an=ran1,n2
explicit formula for nth term of a geometric sequence an=a1rn1

Key Concepts

  • A geometric sequence is a sequence in which the ratio between any two consecutive terms is a constant.
  • The constant ratio between two consecutive terms is called the common ratio.
  • The common ratio can be found by dividing any term in the sequence by the previous term.
  • The terms of a geometric sequence can be found by beginning with the first term and multiplying by the common ratio repeatedly.
  • A recursive formula for a geometric sequence with common ratio r is given by an=ran1 for n2 .
  • As with any recursive formula, the initial term of the sequence must be given.
  • An explicit formula for a geometric sequence with common ratio r is given by an=a1rn1.
  • In application problems, we sometimes alter the explicit formula slightly to an=a0rn.

Glossary

common ratio the ratio between any two consecutive terms in a geometric sequence

geometric sequence a sequence in which the ratio of a term to a previous term is a constant