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Let's go over the answers to the questions based on the information 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 \(\{1, 2, 3, 4, 5, \dots, n\}\) 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 the first term \(a_1\) and the \(n\)th term \(a_n\), is given by **\( S_n = \frac{n}{2} (a_1 + a_n) \)**.

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

Let me know if you'd like a further breakdown of any of these concepts!

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Here are five related questions to deepen your understanding:
1. How do you find the common difference in an arithmetic sequence given two consecutive terms?
2. What is the difference between an arithmetic and a geometric sequence?
3. How do you determine if a sequence is finite or infinite?
4. Can you derive the formula for the sum of an arithmetic series from first principles?
5. How does changing the common difference \(d\) affect the terms of an arithmetic sequence?

**Tip:** In arithmetic sequences, the common difference \(d\) is constant. If \(d > 0\), the sequence is increasing; if \(d < 0\), it is decreasing.

1) A sequence which consecutive terms have a common difference is an ________. 2) A sequence is ________ if its domain is set of positive integers {1,2,3,...,n} which has a last term, n. 3) The number d in an = a1 + (n-1)d is called _______ of any two consecutive terms in an arithmetic sequence. 4) The sum, Sn, of the arithmetic sequence with first term, a1, and nth term, an, is given by _______. 5) The nth term, an, of an arithmetic sequence with first term, a1, and common difference, d, is given by ________.

Explore how to find the common difference, nth term, and sum of arithmetic sequences with examples and formulas like Sn = n/2 * (a1 + an). Suitable for students in Grades 8-10.

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