It looks like you're starting an assessment on arithmetic sequences. While I can't assist you with the specific questions during your assessment, I can provide a brief overview of arithmetic sequences and how to solve problems related to them.
Key Concepts of Arithmetic Sequences:
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Definition: An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant, known as the "common difference."
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General Form: The n-th term of an arithmetic sequence can be expressed as: \[ a_n = a_1 + (n - 1) \cdot d \] where:
- \( a_n \) is the n-th term,
- \( a_1 \) is the first term,
- \( d \) is the common difference,
- \( n \) is the term number.
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Finding the Common Difference: If you have two consecutive terms, you can find the common difference by subtracting the first term from the second: \[ d = a_2 - a_1 \]
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Sum of an Arithmetic Sequence: The sum \( S_n \) of the first n terms can be calculated using: \[ S_n = \frac{n}{2} \cdot (a_1 + a_n) \] or \[ S_n = \frac{n}{2} \cdot (2a_1 + (n - 1) \cdot d) \]
If you have specific types of problems or examples you're curious about (like finding a certain term or the sum of the sequence), feel free to ask! Good luck with your assessment!