The 15th term is the sum of the 13th term and the 14th term.Īnswer: The 15th term of the Fibonacci sequence is 377.Ī recursive formula defines a sequence by expressing each term based on prior terms. Using the recursive formula for the Fibonacci sequence, d=a 2 −a 1 =6−1=5Įxample 3: Given the 13th and 14th terms of the Fibonacci sequence as 144 and 233 respectively, finding the 15th term. Solution: Let a n be the nth term of the sequence, and d be the common difference. Recursive Formula Solved ExamplesĮxample 1: Given the recursive formula f(x)=5f(x−2)+3 and f(0)=0, finding the value of f(8).Įxample 2: Finding the recursive formula for the arithmetic sequence: 1, 6, 11, 16 …. The practical applications of these recursive formulas will be explored in the subsequent section. The formula to discover the nth term of a Fibonacci sequence is:Ī n signifies the nth term within the sequence. Recursive Formula for Fibonacci Sequences Where: a n represents the nth term of a geometric progression (G.P.). The formula to find the nth term of a geometric sequence is: Recursive Formula for Geometric Sequences Where: a n represents the nth term of an arithmetic progression (A.P.). The formula to determine the nth term of an arithmetic sequence is: Recursive Formulas Various types of sequences possess distinct recursive formulas, outlined as follows: Recursive Formula for Arithmetic Sequences The pattern rule that derives any term based on its preceding term(s). It covers two critical parameters: The initial term of the sequence. Understanding Recursive FormulasĪ recursive formula defines each term within a sequence based on preceding terms. Where a i ≥0 and at least one of the a i is greater than 0. In other words, it establishes the next term by relying on one or more known preceding terms.Ī recursive function, represented as h(x), can be articulated as: A recursive function defines each term within a sequence based on a previously known term. Recursive Formula: Before exploring the recursive formula, it’s essential to revisit the concept of a recursive function. Recursive Formula for Fibonacci Sequences.Recursive Formula for Geometric Sequences.Recursive Formula for Arithmetic Sequences.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |