A geometric sequence is a sequence in which the ratio between any two consecutive terms is a constant.<\/li>\n\t
The constant ratio between two consecutive terms is called the common ratio.<\/li>\n\t
The common ratio can be found by dividing any term in the sequence by the previous term.<\/li>\n\t
The terms of a geometric sequence can be found by beginning with the first term and multiplying by the common ratio repeatedly.<\/li>\n\t
A recursive formula for a geometric sequence with common ratio [latex]r[\/latex] is given by [latex]{a}_{n}=r{a}_{n - 1}[\/latex] for [latex]n\\ge 2[\/latex] .<\/li>\n\t
As with any recursive formula, the initial term of the sequence must be given.<\/li>\n\t
An explicit formula for a geometric sequence with common ratio [latex]r[\/latex] is given by [latex]{a}_{n}={a}_{1}{r}^{n - 1}[\/latex].<\/li>\n\t
In application problems, we sometimes alter the explicit formula slightly to [latex]{a}_{n}={a}_{0}{r}^{n}[\/latex].<\/li>\n<\/ul>
Glossary<\/h2>\n
common ratio<\/dt>
the ratio between any two consecutive terms in a geometric sequence<\/dd><\/dl>
geometric sequence<\/dt>
a sequence in which the ratio of a term to a previous term is a constant<\/dd><\/dl>","rendered":"
Key Equations<\/h2>\n
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recursive formula for [latex]nth[\/latex] term of a geometric sequence<\/td>\n
A geometric sequence is a sequence in which the ratio between any two consecutive terms is a constant.<\/li>\n
The constant ratio between two consecutive terms is called the common ratio.<\/li>\n
The common ratio can be found by dividing any term in the sequence by the previous term.<\/li>\n
The terms of a geometric sequence can be found by beginning with the first term and multiplying by the common ratio repeatedly.<\/li>\n
A recursive formula for a geometric sequence with common ratio [latex]r[\/latex] is given by [latex]{a}_{n}=r{a}_{n - 1}[\/latex] for [latex]n\\ge 2[\/latex] .<\/li>\n
As with any recursive formula, the initial term of the sequence must be given.<\/li>\n
An explicit formula for a geometric sequence with common ratio [latex]r[\/latex] is given by [latex]{a}_{n}={a}_{1}{r}^{n - 1}[\/latex].<\/li>\n
In application problems, we sometimes alter the explicit formula slightly to [latex]{a}_{n}={a}_{0}{r}^{n}[\/latex].<\/li>\n<\/ul>\n
Glossary<\/h2>\n
\n
common ratio<\/dt>\n
the ratio between any two consecutive terms in a geometric sequence<\/dd>\n<\/dl>\n
\n
geometric sequence<\/dt>\n
a sequence in which the ratio of a term to a previous term is a constant<\/dd>\n<\/dl>\n\n\t\t\t \n\t\t\t