Math Problem Statement
Solution
To determine which function defines the sequence and also satisfies , let's analyze the given options and the properties of the sequence.
Step 1: Identifying the Sequence Pattern
The sequence provided is . Observing the differences between terms:
The sequence has a common difference of , which indicates that it is an arithmetic sequence with a slope of .
Step 2: Applying the Linear Function Form
For an arithmetic sequence, a function describing it can be in the form: where is the common difference (slope). Here, , so we start with:
Step 3: Finding the Value of
Since , we substitute and into the function:
Thus, the function is:
Step 4: Verifying the Answer
Looking at the options, the correct choice is:
Would you like further details, or do you have any questions?
Here are some related questions you might explore:
- How would the function change if the common difference were different?
- Can you use this method to define other types of sequences?
- What would the function be if instead?
- How do you determine the common difference in sequences?
- What would the function look like if the sequence were geometric?
Tip: For arithmetic sequences, finding the common difference is essential to defining the sequence with a linear function.
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Math Problem Analysis
Mathematical Concepts
Arithmetic Sequence
Linear Functions
Formulas
f(x) = mx + b
Theorems
-
Suitable Grade Level
Grades 7-9
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