What is a formula for the nth term of the given sequence?

−11,−7,−3...

To find the formula for the \(n\)th term of the given sequence \(-11, -7, -3, \ldots\), we first need to determine the pattern or rule that defines the sequence. This sequence appears to be arithmetic, where the difference between consecutive terms is constant.

### Step-by-Step Solution

1. **Identify the common difference:**

   To confirm that the sequence is arithmetic, calculate the difference between consecutive terms:

   \[
   -7 - (-11) = -7 + 11 = 4
   \]

   \[
   -3 - (-7) = -3 + 7 = 4
   \]

   The common difference \(d\) is \(4\).

2. **Find the first term:**

   The first term \(a_1\) of the sequence is \(-11\).

3. **Use the formula for the nth term of an arithmetic sequence:**

   The formula for the nth term of an arithmetic sequence is given by:

   \[
   a_n = a_1 + (n-1)d
   \]

   Here:
   - \(a_1 = -11\) (the first term)
   - \(d = 4\) (the common difference)

4. **Substitute the values into the formula:**

   \[
   a_n = -11 + (n-1) \cdot 4
   \]

5. **Simplify the formula:**

   \[
   a_n = -11 + 4n - 4 = 4n - 15
   \]

### Final Formula

The formula for the \(n\)th term of the sequence \(-11, -7, -3, \ldots\) is:

\[
a_n = 4n - 15
\]

This formula allows you to find any term in the sequence by substituting the value of \(n\).

### Would you like more details or have any questions?

Here are 5 related questions to expand on this topic:

1. What is the formula for the sum of the first \(n\) terms of an arithmetic sequence?
2. How do you find the common difference in an arithmetic sequence if it is not given directly?
3. Can you explain the difference between arithmetic and geometric sequences?
4. How would you determine the 10th term of this sequence using the formula \(a_n = 4n - 15\)?
5. What changes in the formula \(a_n = 4n - 15\) if the common difference is changed to \(6\)?

**Tip:** Always double-check the common difference in a sequence to confirm whether it is arithmetic or geometric.

Learn how to find the formula for the nth term of the sequence -11, -7, -3 with a step-by-step solution. This problem covers arithmetic sequences, including identifying the common difference and using the nth term formula. Suitable for students in Grades 7-9.

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