A student is writing the terms of an arithmetic sequence. The 3rd term is 22 and the 7th term is 42. Write the recursive formula for the sequence. ___________.
Answer & Analysis
Analysis
Question Analysis
This question requires students to find the common difference and the first term of an arithmetic sequence given two terms and then write the recursive formula.
Key Concept Explanation
The common difference in an arithmetic sequence is the constant difference between consecutive terms. The recursive formula for an arithmetic sequence is , .
Step-by-step Solution
1. Identify the given terms: and .
2. Use the relationship between the terms to find the common difference : .
3. Substitute the known values: .
4. Solve for :
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