Math Problem Statement
Solution
The sequence provided is quadratic, meaning its th term can be expressed in the form:
where is a constant to be determined.
From the table:
Position | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|
Term | 4 | 10 | 18 | 28 | 40 |
The general formula starts with , so we first calculate for each value of :
- For :
- For :
- For :
- For :
- For :
Next, subtract from each corresponding term to find the remainder:
- For :
- For :
- For :
- For :
- For :
This shows that the difference between the term and is increasing by 3 each time, which suggests a linear relationship. The additional term is .
Thus, the th term rule for this sequence is:
Would you like any further clarification?
Here are 5 related questions:
- What is the next term in this quadratic sequence?
- How do you find the difference between terms in a quadratic sequence?
- What role does the constant play in the general formula of a quadratic sequence?
- Can you derive a general method for finding the quadratic sequence rule from any given set of terms?
- How would this method apply to sequences that are not quadratic but cubic?
Tip: When analyzing sequences, always check if differences between terms are constant or if they follow a pattern that hints at a higher-degree polynomial relationship.
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Math Problem Analysis
Mathematical Concepts
Quadratic Sequences
Sequences and Series
Algebra
Formulas
nth term formula: n^2 + cn
Difference method for quadratic sequences
Theorems
Quadratic sequence properties
Suitable Grade Level
Grades 8-10
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