A pattern that not only continue the pattern but find the value for the given term in the pattern.
An explicit pattern is a pattern that start at one number but it doesn't increase by it.
The answer depends on what the explicit rule is!
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.
An explicit rule defines the terms of a sequence in terms of some independent parameter. A recursive rule defines them in relation to values of the variable at some earlier stage(s) in the sequence.
An explicit rule is a rule that you can solve without needing the previous term. For example to find the value of y, you don't need to know what x is. y = 4 + 4 vs. y = 2x + 4
well my rule is nothing explicit
Each number is -4 times the previous one. That means that you can write a recursive rule as: f(1) = -3 f(n) = -4 * f(n-1) The explicit rule involves powers of -4; you can write it as: f(n) = -3 * (-4)^(n-1)
Each number is -4 times the previous one. That means that you can write a recursive rule as: f(1) = -3 f(n) = -4 * f(n-1) The explicit rule involves powers of -4; you can write it as: f(n) = -3 * (-4)^(n-1)
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.
The sequence 3, 7, 11, 15 is an arithmetic sequence where each term increases by 4. The recursive rule can be expressed as ( a_n = a_{n-1} + 4 ) with ( a_1 = 3 ). The explicit rule for the nth term is ( a_n = 3 + 4(n - 1) ) or simplified, ( a_n = 4n - 1 ).
In linear algebra, Cramer's rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution.
explain how to find the rule in a numerical pattern