Recursive Formula Math Definition

Applying a rule or formula to its results again and again.

Recursive formula math definition. We double 1 to get 2 then take that result of 2 and apply double again to get 4 then take the 4 and double it to get 8 and so on see. Recursive function in logic and mathematics a type of function or expression predicating some concept or property of one or more variables which is specified by a procedure that yields values or instances of that function by repeatedly applying a given relation or routine operation to known values of the function. A recursive function can also be defined for a geometric sequence where the terms in the sequence have a common factor or common ratio between them. A 4 2a 3 1 87.

A recursive formula is a formula that requires the computation of all previous terms in order to find the value of a n. The recursive formula for a geometric sequence it is easier to create recursive formulas for most geometric sequences than an explicit formula. Then a recursive formula for this sequence will be needed to compute all the previous terms and find the value of t n. If t 1 t 2 t 3 t n is a set of series or a sequence.

A 3 2a 2 1 43. As you can observe from the sequence itself it is an arithmetic sequence which includes the first term followed by other terms and a common difference d between each term is the number you add or subtract to them. A n r a n 1. Let us look at a recursive function example for geometric series.

1 2 4 8 16 32. In mathematics and computer science a recursive definition or inductive definition is used to define the elements in a set in terms of other elements in the set aczel 1977 740ff. The recursive formula is a formula used to determine the subsequent term of a mathematical sequence using one or multiple of the preceding terms. And it can be written as.

3 6 12 24. The formula is commonly used in mathematical logic and computer science to define an object with regards to its own properties. In this the common ratio can be seen easily and can be used to create the recursive formula quickly. Some examples of recursively definable objects include factorials natural numbers fibonacci numbers and the cantor ternary set.

Recursion is an example of an iterative procedure. Start with 1 and apply double recursively. Let a 1 10 and a n 2a n 1 1. T n t n 1.

A n. A 2 2a 1 1 21.