Wager Mage
Wager Mage
Photo: Aleksandar Pasaric
The sequence follows the rule that each number is equal to the sum of the preceding two numbers. The Fibonacci sequence begins with the following 14 integers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233 ...
What is your location? The phrase essentially means, “What is your location?” or “Identify your position,” but is a corrupted phrase from the...
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Problem gamblers may spend 10 to 20 hours or more a week gambling. They also spend a lot of time thinking and worrying about their gambling.
Read More »What is the Fibonacci sequence? The Fibonacci sequence is a set of integers (the Fibonacci numbers) that starts with a zero, followed by a one, then by another one, and then by a series of steadily increasing numbers. The sequence follows the rule that each number is equal to the sum of the preceding two numbers. The Fibonacci sequence begins with the following 14 integers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233 ... Each number, starting with the third, adheres to the prescribed formula. For example, the seventh number, 8, is preceded by 3 and 5, which add up to 8. The sequence can theoretically continue to infinity, using the same formula for each new number. Some resources show the Fibonacci sequence starting with a one instead of a zero, but this is fairly uncommon. Calculating the Fibonacci sequence The Fibonacci sequence can be calculated mathematically. In this approach, each number in the sequence is considered a term, which is represented by the expression F n . The n reflects the number's position in the sequence, starting with zero. For example, the sixth term is referred to as F 5 , and the seventh term is referred to as F 6 . Using this numbering, the Fibonacci sequence can be defined by the following three equations: F 0 = 0 (applies only to the first integer) = 0 (applies only to the first integer) F 1 = 1 (applies only to the second integer) = 1 (applies only to the second integer) F n = F n-1 + F n-2 (applies to all other integers) The first two equations are essentially stating that the term in the first position equals 0 and the term in the second position equals 1. The third equation is a recursive formula, which means that each number of the sequence is defined by using the preceding numbers. For example, to define the fifth number (F 4 ), the terms F 2 and F 3 must already be defined. These two numbers, in turn, require that the numbers preceding them are already defined. The numbers continuously build on each other throughout the sequence. The following table shows the position of each term, along with its F n value and Fibonacci number, starting with the first term and ending with the 14th. Term position F n value Fibonacci number 1st F 0 0 2nd F 1 1 3rd F 2 1 4th F 3 2 5th F 4 3 6th F 5 5 7th F 6 8 8th F 7 13 9th F 8 21 10th F 9 34 11th F 10 55 12th F 11 89 13th F 12 144 14th F 13 233 You can try out the formula for yourself, using the table to find the sequence numbers preceding the target term value. For example, the following calculation finds the Fibonacci number for the term in the tenth position (F 9 ): F 9 = F 9-1 + F 9-2 = F 8 + F 7 = 21 + 13 = 34 The challenge with a recursive formula is that it always relies on knowing the previous Fibonacci numbers in order to calculate a specific number in the sequence. For example, you can't calculate the value of the 100th term without knowing the 98th and 99th terms, which requires that you know all the terms before them. There are other equations that can be used, however, such as Binet's formula, a closed-form expression for finding Fibonacci sequence numbers. Another option it to program the logic of the recursive formula into application code such as Java, Python or PHP and then let the processor do the work for you.
bogie (plural bogies) (chiefly US, slang) A marijuana cigarette; a joint. quotations ▼synonym ▲ Synonyms: see Thesaurus:marijuana cigarette.
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