The Fibonacci sequence is listed below: The first and second numbers both start at 1. After that, each number in the series is the sum of the two preceding numbers. Here is an example: 1, 1, 2, 3, 5, 8, 13, 21, ... If F(n) is the nth value in the sequence, then this definition can be expressed as F(1) = 1 F(2) = 1 F(3) = 2 F(4) = 3 F(5) = 5 F(6) = 8 F(7) = 13 F(8) = 21 F(n) = F(n - 1) + F(n - 2) for n > 2 Example: Given n with a value of 4 F(4) = F(4-1) + F(4-2) F(4) = F(3) + F(2) F(4) = 2 + 1 F(4) = 3 The value of F at position n is defined using the value of F at two smaller positions. Using the definition of the Fibonacci sequence, determine the value of F(10) by using the formula and the sequence. Show the terms in the Fibonacci sequence and show your work for the formula
The Fibonacci sequence is listed below: The first and second numbers both start at 1. After that, each number in the series is the sum of the two preceding numbers. Here is an example:
1, 1, 2, 3, 5, 8, 13, 21, ...
If F(n) is the nth value in the sequence, then this definition can be expressed as
F(1) = 1
F(2) = 1
F(3) = 2
F(4) = 3
F(5) = 5
F(6) = 8
F(7) = 13
F(8) = 21
F(n) = F(n - 1) + F(n - 2) for n > 2
Example:
Given n with a value of 4
F(4) = F(4-1) + F(4-2)
F(4) = F(3) + F(2)
F(4) = 2 + 1
F(4) = 3
The value of F at position n is defined using the value of F at two smaller positions. Using the definition of the Fibonacci sequence, determine the value of F(10) by using the formula and the sequence. Show the terms in the Fibonacci sequence and show your work for the formula.
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