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The image shows a question asking to find the \(15^{\text{th}}\) term of an arithmetic sequence where the first term is 11 and the common difference is -7. The general formula for the \(n^{\text{th}}\) term of an arithmetic sequence is:

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

Where:
- \(a_n\) is the \(n^{\text{th}}\) term,
- \(a_1\) is the first term,
- \(n\) is the term number, and
- \(d\) is the common difference.

Here, the first term \(a_1 = 11\), the common difference \(d = -7\), and \(n = 15\). Plugging these values into the formula:

\[
a_{15} = 11 + (15-1) \cdot (-7)
\]

Now let's calculate this.The \(15^{\text{th}}\) term of the arithmetic sequence is \(-87\).

Would you like more details or further clarification?

Here are 5 questions related to this:

1. How do you derive the general formula for an arithmetic sequence?
2. What happens to the terms of an arithmetic sequence when the common difference is negative?
3. Can the \(n^{\text{th}}\) term formula be used to find the sum of the first \(n\) terms?
4. How does the value of \(n\) affect the calculation in an arithmetic sequence?
5. Can an arithmetic sequence ever have a common difference of zero?

**Tip**: In an arithmetic sequence, the common difference \(d\) determines whether the sequence is increasing, decreasing, or constant.

Find the 15th term of an arithmetic sequence where the first term is 11 and the common difference is -7.

This page provides a detailed solution for finding the 15th term of an arithmetic sequence where the first term is 11 and the common difference is -7. Learn how to apply the general formula for arithmetic sequences to solve this problem. Suitable for students in Grades 7-9.

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