Math Problem Statement
Here is a rule to make a list of nujmbers: Each numbe is the sum of the previous two numbers. Start with the nuumbers 0 and 1, then follow the rule to build a sequence of 10 numbers
Solution
To create the sequence based on the rule provided:
- Start with the numbers 0 and 1.
- Each subsequent number is the sum of the previous two numbers.
Let's build the sequence:
- First number: (Given)
- Second number: (Given)
- Third number:
- Fourth number:
- Fifth number:
- Sixth number:
- Seventh number:
- Eighth number:
- Ninth number:
- Tenth number:
The sequence of 10 numbers is:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34
Would you like any more details or explanations?
Here are five related questions:
- What is the name of this sequence?
- How would you find the 20th number in the sequence?
- What is the formula for finding any term in this sequence without listing all the previous terms?
- How does the ratio between consecutive terms of the sequence behave as the sequence progresses?
- Can you identify a pattern in the differences between consecutive numbers in the sequence?
Tip: The sequence you just created is known as the Fibonacci sequence, which has many interesting properties and appears in various fields of mathematics, nature, and art.
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Math Problem Analysis
Mathematical Concepts
Number Sequences
Fibonacci Sequence
Formulas
-
Theorems
Fibonacci Sequence Properties
Suitable Grade Level
Grades 6-8
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