![]() □ = 1 into the recursive formula □ = □ − 4 To find the second term, □ , we substitute Sequence defined by the recursive formula Note that this is actually anĪrithmetic sequence with a first term of 10 and a common difference of 1.Īs another example, suppose we are asked to find the first five terms of the Therefore, the first four terms of this sequence are ![]() Into the formula and use the fact that □ = 1 2 to get Into the formula and use the fact that □ = 1 1 to getįinally, to find □ , we substitute □ = 3 Similarly, to find □ , we substitute □ = 2 To find the second term, □ , we substitute □ = 1 into the recursive formula We already know the first term, which is □ = 1 0 . Suppose we areĪsked to find the first four terms of the sequence defined by the recursive This process is best illustrated through some specific examples. In this way, we canīuild up the sequence until it has as many terms as we wish. ![]() The formula with □ = 2 to derive the value of Once we know the value of □ , we can use □ = □ ( □ ) , we can use the formula with If we know the first term, □ , and the recursive formula ![]() To generate a sequence from its recursive formula, we need to know the first Of a sequence using a preceding term or terms.Ī recursive formula of the form □ = □ ( □ ) ĭefines each term of a sequence as a function of the previous term. Definition: Recursive Formula of a SequenceĪ recursive formula (sometimes called a recurrence relation) is a formula that ![]()
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