Concept explainers
(a)
To write recursive rule for the lengths of the bones
(a)
Answer to Problem 52E
Recursive rule for the lengths of the bones
Explanation of Solution
Given:
The X-ray shows the lengths (in centimetres) of bones in a human hand.
Concept Used:
Fibonacci sequence: a sequence of numbers in which each number (Fibonacci number) is the sum of the two preceding numbers.
Calculation:
Given sequence
Therefore the sequence is Fibonacci sequence
Recursive rule for the lengths of bones is
Conclusion:
Recursive rule for the lengths of bones is
(b)
To measure different sections of hand and tell if they sequence can be represented by a recursively defined sequence
(b)
Answer to Problem 52E
Yes, lengths can be represented by a recursively defined sequence
Explanation of Solution
Given:
Measure the lengths of different sections of hand
Concept Used:
Fibonacci series: A series of numbers in which each number (Fibonacci number) is the sum of the two preceding numbers
Calculation:
Folding first finger in form of spiral and measuring different sections to get sequence
Also,
Hence,
These are Fibonacci numbers, so the sequence is Fibonacci sequence
Therefore,
Sequence can be defined recursively.
Conclusion:
Yes, lengths can be represented by a recursively defined sequence
Chapter 6 Solutions
BIG IDEAS MATH Integrated Math 1: Student Edition 2016
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