Question

Create your own arithmetic sequence. List at least six terms of your sequence.
Explain what makes it arithmetic.

Answer 1

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This constant difference is known as the "common difference."

Here’s an example of an arithmetic sequence:

**Sequence:** 3, 7, 11, 15, 19, 23

**Common Difference:** The difference between consecutive terms is 4 (7 - 3 = 4, 11 - 7 = 4, 15 - 11 = 4, 19 - 15 = 4, 23 - 19 = 4).

**Explanation of what makes it arithmetic:**
1. **Constant Difference:** In this sequence, the difference between each pair of consecutive terms is always the same (4 in this case). This is the defining characteristic of arithmetic sequences.
2. **Linear Relationship:** If you were to graph the terms of the sequence, they would form a straight line, demonstrating a linear relationship between the terms.
3. **Formula:** The n-th term of an arithmetic sequence can be expressed using the formula:
\[
a_n = a_1 + (n - 1) \cdot d
\]
where \( a_1 \) is the first term, \( d \) is the common difference, and \( n \) is the term number. For this sequence, \( a_1 = 3 \) and \( d = 4 \).

Thus, the given sequence (3, 7, 11, 15, 19, 23) is an arithmetic sequence with a common difference of 4.