Sequence formulas direct and recursive
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The document discusses sequence formulas, including direct and recursive formulas. It provides examples of sequences defined by direct formulas like the sequence where the nth term is defined as An = 9n + 3. It then explains that a recursive formula defines each term of a sequence using preceding terms, and must state the initial term(s). It gives examples of calculating sequence terms using general formulas and recursion equations. Finally, it briefly mentions the famous Fibonacci sequence and its applications.
![EXAMPLE 1.2.
[Fibonacci sequence] Consider the following recursion equation.
The Fibonacci sequence has a long history in mathematics, and you can find out more about it online at any
number of websites. The Fibonacci sequence is named after the 13th-century Italian mathematician known as
Fibonacci, who used it to solve a problem concerning the breeding of rabbits. This sequence also occurs in
numerous applications in plant biology.](https://image.slidesharecdn.com/sequenceformulasdirectandrecursive-201208095621/85/Sequence-formulas-direct-and-recursive-8-320.jpg)
Sequence formulas direct and recursive
- 1. BUSINESS MATHEMATICS -1 TOPIC : SEQUENCE FORMULAS: DIRECT AND RECURSIVE
- 2. SEQUENCE FORMULAS: DIRECT AND RECURSIVE The final type of GRE formula problem involves sequences. A sequence is a collection of numbers in a set order. The order of a given sequence is determined by a rule. Here are examples of sequence rules: For all integers n ≥ 1… An = 9n + 3 The nth term of this sequence is defined by the rule 9n + 3, for integers n ≥ 1. For example, the fourth term in this sequence is 9n + 3 = 9(4) + 3 = 39. The first ten terms of the sequence are as follows: 12, 21, 30, 39, 48, 57, 66, 75, 84, 93 (notice that successive terms differ by 9)
- 3. WHAT IS A RECURSIVE FORMULA? A recursive formula is a formula that defines each term of a sequence using preceding term(s). Recursive formulas must always state the initial term, or terms, of the sequence.
- 4. WHAT IS THE NTH TERM IN A SEQUENCE? Capturing this pattern in algebra, we write the general (or nth) term of an arithmetic sequence as: an = a1 + (n - 1 ) d. This is the formula that will be used when we find the general (or nth) term of an arithmetic sequence.
- 5. CALCULATE A SEQUENCE The general formula for any sequence involves the letter n, which is the position of the term in the sequence (the first term would be n = 1, and the 20th term would be n = 20), as well as the rule to find each term.
- 6. THE RULES OF SEQUENCE More than 3 must be in teams. No more than 3 teams can play. One player or team must score TWO SEQUENCES before their opponents. A Sequence is a connected series of five of the same color marker chip in a straight line, either up and down, across or diagonally on the playing surface.
- 7. EXAMPLE 1.1. Consider the sequence given by a D 2an1 C 1 with a0 D 4. The recursion function (or recursion equation) tells us how to find a1, a2, and so on.
- 8. EXAMPLE 1.2. [Fibonacci sequence] Consider the following recursion equation. The Fibonacci sequence has a long history in mathematics, and you can find out more about it online at any number of websites. The Fibonacci sequence is named after the 13th-century Italian mathematician known as Fibonacci, who used it to solve a problem concerning the breeding of rabbits. This sequence also occurs in numerous applications in plant biology.
- 9. THANK YOU!