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.

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!