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Here are the answers to the questions shown in the image:

1. A sequence in which consecutive terms have a common difference is an **arithmetic sequence**.

2. A sequence is **finite** if its domain is a set of positive integers {1, 2, 3, 4, 5, ..., n} which has a last term, \( n \).

3. The number \( d \) in \( a_n = a_1 + (n - 1)d \) is called the **common difference** of any two consecutive terms in an arithmetic sequence.

4. The sum, \( S_n \), of the arithmetic sequence with first term, \( a_1 \), and nth term, \( a_n \), is given by \( S_n = \frac{n}{2}(a_1 + a_n) \).

5. The nth term, \( a_n \), of an arithmetic sequence with first term, \( a_1 \), and common difference, \( d \), is given by \( a_n = a_1 + (n - 1)d \).

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Would you like more detailed explanations for these formulas or concepts? 

Here are 5 related questions to further your understanding:
1. How is the formula for the sum of an arithmetic sequence derived?
2. What is the difference between arithmetic and geometric sequences?
3. Can an arithmetic sequence have a negative common difference?
4. How would you find the sum of a sequence if only the first and common difference are given?
5. How does the common difference influence the behavior of an arithmetic sequence?

**Tip:** In an arithmetic sequence, the common difference remains constant, meaning each term increases or decreases by the same amount compared to the previous term.

A sequence which consecutive terms have a common difference is an __________.

Learn about arithmetic sequences, including how to identify them, calculate their common difference, and find their sum. The formulas used include a_n = a_1 + (n - 1)d for the nth term and S_n = (n/2)(a_1 + a_n) for the sum. Suitable for students in Grades 8-10.

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