To solve this problem, let’s determine the nth term rule for the given arithmetic sequence and use it to calculate the 11th term.

Step 1: Identify the common difference

The sequence is:
15, 22, 29, 36

The difference between consecutive terms:
$22 - 15 = 7$
$29 - 22 = 7$
$36 - 29 = 7$

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

Step 2: General formula for the nth term of an arithmetic sequence

The formula for the nth term ($a_n$) of an arithmetic sequence is:
$a_n = a_1 + (n - 1) \cdot d$
where:

• $a_1$ is the first term,
• $d$ is the common difference,
• $n$ is the term number.

Substitute the values $a_1 = 15$ and $d = 7$:
$a_n = 15 + (n - 1) \cdot 7$
Simplify:
$a_n = 15 + 7n - 7 = 7n + 8$

Step 3: Calculate the 11th term

Substitute $n = 11$ into the formula:
$a_{11} = 7(11) + 8$
$a_{11} = 77 + 8 = 85$

Final Answer:

The 11th term of the sequence is 85.

Let me know if you'd like further clarification!

Here are 5 related questions to expand your understanding:

1. How can you find the sum of the first 11 terms of this sequence?
2. What happens if the common difference is negative?
3. Can you derive the formula for the nth term of a geometric sequence?
4. How does the nth term formula help in identifying patterns in data?
5. How can arithmetic sequences be applied in real-world scenarios?

Tip: Always verify the common difference before assuming a sequence is arithmetic. Mis