The common difference of the given sequence is,ĭ = 2 - (-4) (or) 8 - 2 (or) 16 - 8 =. Using Arithmetic Sequence Recursive Formula? What Is the n th Term of the Sequence -4, 2, 8, 16.
Let us learn the arithmetic sequence recursive formula along with a few solved examples. This fixed number is usually known as the common difference and is denoted by d. is an arithmetic sequence as every term is obtained by adding a fixed number 2 to its previous term. It is a sequence of numbers in which every successive term is obtained by adding a fixed number to its previous term. Image Courtesy:ġ.Before going to learn the arithmetic sequence recursive formula, let us recall what is an arithmetic sequence. Reference:ġ.“Recursive Formulas for Arithmetic Sequences.” Khan Academy, Khan Academy, Available here.Ģ.Mathwords: Removable Discontinuity, Available here.ģ.“Explicit Formulas for Arithmetic Sequences.” Khan Academy, Khan Academy, Available here. The main difference between Recursive and Explicit is that Recursive formula gives the value of a specific term based on the previous term while Explicit formula gives the value of a specific term based on the position. A formula can be either recursive or explicit. We can represent a sequence using a formula. Hence, this is another difference between recursive and explicit. However, in an explicit formula, we can find the value of a term in the sequence using its position. In a recursive formula, we can find the value of a term in the sequence using the value of the previous term. Thus, this is the main difference between recursive and explicit. For a sequence a1, a2, a3… a n, explicit formula is a formula that can compute the value of a n using its location. Difference Between Recursive and Explicit Definitionįor a sequence a 1, a 2, a 3… a n, a recursive formula is a formula that requires the computation of all previous terms in order to find the value of a n. When observing the sequence, it can be seen that it is possible to calculate the value of a specific term using the position. Likewise, we can find the values of any term in the sequence. In explicit formulas, we can find the value of a specific term based on its position. That is the functionality of recursive formulas. Therefore, it requires the previous term or terms to find the value of a specific term.
To find a (3), we need the value of a (2) and to find the value a (2), we need the value of a(1). To find a (4), we need the value of a(3). Likewise, we can calculate the values of the terms in the sequence.
Similarly, we can find the third term as follows.
We can substitute value to the above formula. In a recursive formula, we can find the value of a specific term based on the previous term.įor example, assume a formula as follows. – Comparison of Key Differences Key Terms Difference Between Recursive and Explicit A formula describes a way of finding any term in the sequence. There are two types of formulas as recursive and explicit formulas. In other words, we can directly compute any term of the sequence using a formula. We can represent an arithmetic sequence using a formula. It refers to a set of numbers placed in order. The above formula for finding the n t h term of an arithmetic sequence is used to find any term of the sequence when the values of 'a 1 ' and 'd' are known. The main difference between recursive and explicit is that a recursive formula gives the value of a specific term based on the previous term while an explicit formula gives the value of a specific term based on the position.Ī sequence is an important concept in mathematics.
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