Concept explainers
(a)
To write sequence in which each term
(a)
Answer to Problem 54E
Sequence in which each term
Explanation of Solution
Given:
Squares in following diagram
Concept Used:
Fibonacci series: A series of numbers in which each number (Fibonacci number) is the sum of the two preceding numbers.
Calculation:
From the given figure taking length of square sides in the order form a sequence of squares
Conclusion:
Sequence in which each term
(b)
To write name of sequence and determine next term of sequence
(b)
Answer to Problem 54E
Sequence obtained in part (a) is
As
Therefore,
These are Fibonacci numbers
Therefore recursive rule is given by
Name of the sequence is Fibonacci sequence
Next term of the sequence is 13
Explanation of Solution
Given:
Squares in following diagram
Concept Used:
Fibonacci series: a series of numbers in which each number (Fibonacci number) is the sum of the two preceding numbers.
Calculation:
Sequence obtained is
This sequence satisfies condition of Fibonacci series
Hence,
Given sequence is Fibonacci sequence
The next term of this sequence is sum of previous two
Therefore,
Next term = 8+5 = 13
Conclusion:
Name of the sequence is Fibonacci sequence
Next term of the sequence is 13
(c)
To add another square in the given diagram
(c)
Answer to Problem 54E
Explanation of Solution
Given:
Squares in following diagram
Concept Used:
Using next term obtained in part (b)
Calculation:
From the sequence
Next Square to drawn will have 13 as its side
Therefore,
Diagram obtained is given below
Chapter 6 Solutions
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