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Study Guides > College Algebra

Key Concepts & Glossary

Key Equations

recursive formula for nthnth term of a geometric sequence an=ran1,n2{a}_{n}=r{a}_{n - 1},n\ge 2
explicit formula for nthnth term of a geometric sequence an=a1rn1{a}_{n}={a}_{1}{r}^{n - 1}

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 rr is given by an=ran1{a}_{n}=r{a}_{n - 1} for n2n\ge 2 .
  • As with any recursive formula, the initial term of the sequence must be given.
  • An explicit formula for a geometric sequence with common ratio rr is given by an=a1rn1{a}_{n}={a}_{1}{r}^{n - 1}.
  • In application problems, we sometimes alter the explicit formula slightly to an=a0rn{a}_{n}={a}_{0}{r}^{n}.

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

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