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.