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Test I: Identify Me!

1. Common Difference: This refers to the constant difference between any two consecutive terms in an arithmetic sequence.
2. Arithmetic Sequence: A sequence where the difference between consecutive terms is constant.
3. The formula $a_n = a_1 + (n - 1)d$ represents the nth term of an arithmetic sequence.
4. Sum of an arithmetic sequence: Given as $S_n = \frac{n}{2}(a_1 + a_n)$.
5. nth term formula: $a_n = a_1 + (n - 1)d$.

Test II: Multiple Choice

Here are some solutions to a few of the questions: 6. Common difference in the sequence $-15, -11, -7, -3, \dots$ is 4. 7. The set of first four terms for the sequence $a_n = 7n + 4$ is c. 11, 18, 25, 32. 8. Formula for the nth term in $-1, 2, 5, 8, 11, \dots$ is $a_n = 3n - 4$. 9. First term of the arithmetic sequence $\_, 7, 11, 15, 19$ is 3. 10. Arithmetic sequence: $1, -1, -3, -5, \dots$, option b..

Would you like more detailed answers for any specific questions from the test? Here are five follow-up questions that relate to the topic of arithmetic sequences:

1. How do you derive the formula for the sum of an arithmetic sequence?
2. How do you find the common difference if you're only given non-consecutive terms of the sequence?
3. What are the conditions that define whether a sequence is arithmetic or not?
4. How would you find the nth term of an arithmetic sequence if the first term is negative?
5. How is the arithmetic mean of a sequence related to the common difference?

Tip: When working with arithmetic sequences, always try to identify the common difference first. It will help in determining the nth term and sum more easily.