An arithmetic sequence is a sequence where the difference between any two consecutive terms is a constant.<\/li>\n \t
The constant between two consecutive terms is called the common difference.<\/li>\n \t
The common difference is the number added to any one term of an arithmetic sequence that generates the subsequent term.<\/li>\n \t
The terms of an arithmetic sequence can be found by beginning with the initial term and adding the common difference repeatedly.<\/li>\n \t
A recursive formula for an arithmetic sequence with common difference [latex]d[\/latex] is given by [latex]{a}_{n}={a}_{n - 1}+d,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 an arithmetic sequence with common difference [latex]d[\/latex] is given by [latex]{a}_{n}={a}_{1}+d\\left(n - 1\\right)[\/latex].<\/li>\n \t
An explicit formula can be used to find the number of terms in a sequence.<\/li>\n \t
In application problems, we sometimes alter the explicit formula slightly to [latex]{a}_{n}={a}_{0}+dn[\/latex].<\/li>\n<\/ul>\n
Glossary<\/h2>\narithmetic sequence<\/strong> a sequence in which the difference between any two consecutive terms is a constant\n\ncommon difference<\/strong> the difference between any two consecutive terms in an arithmetic sequence\n","rendered":"
Key Equations<\/h2>\n
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recursive formula for nth term of an arithmetic sequence<\/td>\n
[latex]{a}_{n}={a}_{n - 1}+d \\text{ for } n\\ge 2[\/latex]<\/td>\n<\/tr>\n
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explicit formula for nth term of an arithmetic sequence<\/td>\n
An arithmetic sequence is a sequence where the difference between any two consecutive terms is a constant.<\/li>\n
The constant between two consecutive terms is called the common difference.<\/li>\n
The common difference is the number added to any one term of an arithmetic sequence that generates the subsequent term.<\/li>\n
The terms of an arithmetic sequence can be found by beginning with the initial term and adding the common difference repeatedly.<\/li>\n
A recursive formula for an arithmetic sequence with common difference [latex]d[\/latex] is given by [latex]{a}_{n}={a}_{n - 1}+d,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 an arithmetic sequence with common difference [latex]d[\/latex] is given by [latex]{a}_{n}={a}_{1}+d\\left(n - 1\\right)[\/latex].<\/li>\n
An explicit formula can be used to find the number of terms in a sequence.<\/li>\n
In application problems, we sometimes alter the explicit formula slightly to [latex]{a}_{n}={a}_{0}+dn[\/latex].<\/li>\n<\/ul>\n
Glossary<\/h2>\n
arithmetic sequence<\/strong> a sequence in which the difference between any two consecutive terms is a constant<\/p>\n
common difference<\/strong> the difference between any two consecutive terms in an arithmetic sequence<\/p>\n\n\t\t\t \n\t\t\t