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The problem asks you to calculate the 11th term of the arithmetic sequence based on the first few terms: 15, 22, 29, and 36. Let's break this down step-by-step.

### Step 1: Find the common difference
This is an arithmetic sequence, so the difference between each consecutive term is constant. To find the common difference:

- \( 22 - 15 = 7 \)
- \( 29 - 22 = 7 \)
- \( 36 - 29 = 7 \)

So, the common difference \( d \) is 7.

### Step 2: Find the nth term formula
The general formula for the nth term of an arithmetic sequence is:

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

Where:
- \( a_n \) is the nth term,
- \( a_1 \) is the first term,
- \( n \) is the term number, and
- \( d \) is the common difference.

In this case:
- \( a_1 = 15 \),
- \( d = 7 \).

Thus, the nth term formula is:

\[
a_n = 15 + (n - 1) \cdot 7
\]

### Step 3: Calculate the 11th term
To find the 11th term (\( a_{11} \)):

\[
a_{11} = 15 + (11 - 1) \cdot 7
\]
\[
a_{11} = 15 + 10 \cdot 7
\]
\[
a_{11} = 15 + 70
\]
\[
a_{11} = 85
\]

So, the 11th term is **85**.

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Do you have any questions or need further clarification?

Here are some related questions for you:
1. How do you find the nth term of any arithmetic sequence?
2. What happens to the sequence if the common difference is negative?
3. Can you derive the formula for the sum of the first n terms of an arithmetic sequence?
4. How does the nth term formula change if the first term is 0?
5. How do geometric sequences differ from arithmetic sequences?

**Tip**: Always check your common difference first when dealing with arithmetic sequences!

By first working out the nth term rule, calculate the 11th term of this arithmetic sequence: 15, 22, 29, 36.

Learn how to calculate the 11th term of an arithmetic sequence with the formula a_n = a_1 + (n - 1) * d. This example uses the sequence 15, 22, 29, 36 and is suitable for students in Grades 7-9.

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