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.
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.
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)
It is not possible to give a conclusive answer because for a recursive relationship of order 1, the first (or 0th) term must be specified.A(n) = (5*n^2 + 3*n + 2*A(1) - 8)/2 for n = 1, 2, 3, ...
Implicit: x2 + 2y = 5 Explicit : y = (5 - x2)/2
recursive rules need the perivius term explicit dont
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.
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.
What advantages does being able to symbolize your argument provide.
-7
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.
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)
Advantages of communicative language teaching include a focus on communication skills, real-life language use, and student engagement. However, some disadvantages may include a lack of explicit grammar instruction, time-consuming lesson planning, and challenges in assessing progress.
Eiffel is known for its strong emphasis on software reliability and maintainability, featuring design by contract, which enhances program correctness through explicit contracts for classes and methods. Its object-oriented nature promotes code reuse and modularity. However, disadvantages include a smaller community and ecosystem compared to more popular languages, which can limit available libraries and resources. Additionally, the learning curve can be steep for those unfamiliar with its unique syntax and concepts.
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
The question does not make sense."Same as" would mean you want to know what the similarities are."Different from" would mean you want to know how they are different.However, "same from" means neither.