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Answer: An explicit formula for a sequence allows you to find the value of any term in the sequence. ... A recursive formula for a sequence allows you to find the value of the nth term in the sequence if you know the value of the (n-1)th term in the sequence.
An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.
What is an arithmetic sequence?
An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.
The explicit formula for any arithmetic series is given by the formula,
[tex]a_n = a_1 + (n-1)d[/tex]
where d is the difference and a₁ is the first term of the sequence.
The major distinction between recursive and explicit formulas is that a recursive formula returns the value of a particular term depending on the preceding term, whereas an explicit formula returns the value of a given term based on its location.
When the value of the first term and the common difference is known then an explicit formula is used, while the recursive formula will be used when the value of the previous value is known and the value of the common difference is known.
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