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a recursive formula is always based on a preceding value and uses A n-1 and the formula must have a start point (an A1) also known as a seed value.
unlike recursion, explicit forms can stand alone and you can put any value into the "n" and one answer does not depend on the answer before it. we assume the "n" starts with 1 then 2 then 3 and so on
arithmetic sequence: an = a1 + d(n-1) this does not depend on a previous value
What else can I help you with?
Will the explicit formula find the same answer when using the recursive formula?
It is often possible to find an explicit formula that gives the same answer as a given recursive formula - and vice versa. I don't think you can always find an explicit formula that gives the same answer.
What is the difference between a geometric sequence and a recursive formula?
what is the recursive formula for this geometric sequence?
What is the common difference between recursive and explicit arithmetic equations?
The common difference between recursive and explicit arithmetic equations lies in their formulation. A recursive equation defines each term based on the previous term(s), establishing a relationship that builds upon prior values. In contrast, an explicit equation provides a direct formula to calculate any term in the sequence without referencing previous terms. While both methods describe the same arithmetic sequence, they approach it from different perspectives.
What recursive formulas represents the same arithmetic sequence as the explicit formula an 5 n - 12?
-7
What is the difference between a explicit equation and a recursive equation?
An explicit equation defines a sequence by providing a direct formula to calculate the nth term without needing the previous terms, such as ( a_n = 2n + 3 ). In contrast, a recursive equation defines a sequence by specifying the first term and providing a rule to find subsequent terms based on previous ones, such as ( a_n = a_{n-1} + 5 ) with an initial condition. Essentially, explicit equations allow for direct access to any term, while recursive equations depend on prior terms for computation.
Is the explicit rule for a geometric sequence defined by a recursive formula of for which the first term is 23?
Yes, the explicit rule for a geometric sequence can be defined from a recursive formula. If the first term is 23 and the common ratio is ( r ), the explicit formula can be expressed as ( a_n = 23 \cdot r^{(n-1)} ), where ( a_n ) is the nth term of the sequence. This formula allows you to calculate any term in the sequence directly without referencing the previous term.
What is the recursive formula for the sequence 8101214?
The sequence 8101214 appears to follow a pattern based on the difference between consecutive terms. The differences between the terms are 2, 2, 2, which indicates a constant difference. Therefore, the recursive formula can be expressed as ( a_n = a_{n-1} + 2 ), with the initial term ( a_1 = 8 ).
How are recursive and explicit rules the same?
Recursive and explicit rules are both methods used to define sequences in mathematics. They both provide a way to generate terms of a sequence, where a recursive rule defines each term based on previous terms, while an explicit rule provides a formula to calculate any term directly. Despite their different approaches, both types of rules ultimately serve the same purpose: to describe the pattern or relationship within a sequence. Additionally, both can be used to analyze and predict future terms in the sequence.
What is the example of an explicit formula?
An explicit formula is a formula in which depicts relations between the sums over complex number zeros and over prime numbers. An example of an explicit formula is: _(t) = _log(_) + Re(_(1/4 + it/2)).
A certain arithmetic sequence has the recursive formula If the common difference between the terms of the sequence is -11 what term follows the term that has the value 11?
In this case, 22 would have the value of 11.
Why does the explicit rule provide more information about sequences than the recursive rule?
The explicit rule provides a direct formula to calculate any term in a sequence without needing to know the previous terms, allowing for quicker evaluations and a clearer understanding of the sequence's behavior. In contrast, the recursive rule defines each term based on the preceding term, which can be less efficient for finding distant terms and may obscure the overall pattern. This makes the explicit rule particularly useful for analyzing and predicting the long-term behavior of sequences.
What are the advantages and disadvantages of a recursive rule compared to an explicit rule?
Recursive rules define a sequence based on previous terms, making them useful for generating terms step-by-step, which can be intuitive for understanding relationships in sequences. However, they can be less efficient for calculating specific terms, especially for large indices, as they may require multiple calculations. In contrast, explicit rules provide a direct formula for finding any term in the sequence, allowing for quicker calculations. The disadvantage of explicit rules is that they may be more complex to derive and less intuitive for understanding the sequence's progression.
