Math Problem Statement
Find the sixth, seventh, and eighth term of the following sequence: 1,4,9,17,29
Solution
The given sequence is: 1, 4, 9, 17, 29.
Let's identify the pattern by examining the differences between consecutive terms:
The differences between consecutive terms are: 3, 5, 8, 12.
Now, let's look at the differences between these differences:
The second differences are increasing by 1. This indicates that the sequence follows a quadratic pattern.
Finding the next terms:
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The next difference should be .
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Adding this to the last term: .
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The next difference should be .
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Adding this: .
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The next difference should be .
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Adding this: .
Thus, the sixth, seventh, and eighth terms are:
- Sixth term = 46
- Seventh term = 69
- Eighth term = 99
Would you like further details or have any questions?
Here are 5 related questions:
- How can you find the nth term of a quadratic sequence?
- What are the first and second differences in a sequence?
- How do you derive a general formula for a quadratic sequence?
- What are some real-world applications of quadratic sequences?
- How do linear and quadratic sequences differ in terms of growth?
Tip: To identify quadratic sequences, always check for constant second differences!
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Math Problem Analysis
Mathematical Concepts
Sequences
Quadratic Sequences
Algebra
Formulas
Quadratic sequence pattern: Constant second differences
Theorems
Quadratic Growth Theorem
Suitable Grade Level
Grades 7-9
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