The problem asks to calculate the general term of the given arithmetic sequence.

The sequence is: $-13, -7, -1, 5, 11, \dots$

Step 1: Identify the common difference ($d$)

To find the common difference $d$, subtract the first term from the second term: $d = -7 - (-13) = 6$

The common difference is $d = 6$.

Step 2: General formula for an arithmetic sequence

The general term $a_n$ of an arithmetic sequence is given by the formula: $a_n = a_1 + (n-1) \cdot d$ where:

• $a_1$ is the first term of the sequence,
• $d$ is the common difference,
• $n$ is the term number.

Step 3: Substitute the known values

In this case, the first term $a_1 = -13$ and the common difference $d = 6$. Substituting these into the general formula: $a_n = -13 + (n-1) \cdot 6$ Simplifying: $a_n = -13 + 6n - 6$ $a_n = 6n - 19$

Conclusion:

The general term of the arithmetic sequence is: $a_n = 6n - 19$

Let me know if you want further details on this, or if you have any questions!

Here are 5 questions to extend this problem:

1. How would you find the 10th term of this arithmetic sequence?
2. What is the sum of the first 20 terms of this arithmetic sequence?
3. If the general term is $a_n = 6n - 19$, what is the value of $n$ when the term is 53?
4. How does changing the common difference $d$ affect the general term of the sequence?
5. What is the relationship between the common difference and the slope of the linear representation of the sequence?

Tip: Always check the common difference carefully, as it determines the rate at which terms change in an arithmetic sequence.