etermine	the	fifteenth term	of	the	arithmetic	sequence	in	which	the	first	term	is	5	
and	the	eighth term	is	33. 

To find the fifteenth term of the arithmetic sequence, we need to determine the common difference \(d\) and then use the formula for the general term of an arithmetic sequence:

\[
a_n = a_1 + (n-1) \cdot d
\]
where:
- \(a_n\) is the \(n\)-th term,
- \(a_1\) is the first term,
- \(d\) is the common difference,
- \(n\) is the term number.

### Step 1: Use the given information
We are told:
- The first term \(a_1 = 5\),
- The eighth term \(a_8 = 33\).

We can apply the general formula for the 8th term:
\[
a_8 = a_1 + (8-1) \cdot d
\]
\[
33 = 5 + 7d
\]
Solving for \(d\):
\[
33 - 5 = 7d
\]
\[
28 = 7d
\]
\[
d = 4
\]

### Step 2: Find the 15th term
Now that we know the common difference \(d = 4\), we can find the 15th term using the formula:
\[
a_{15} = a_1 + (15-1) \cdot d
\]
\[
a_{15} = 5 + 14 \cdot 4
\]
\[
a_{15} = 5 + 56
\]
\[
a_{15} = 61
\]

### Final Answer:
The fifteenth term of the arithmetic sequence is \( \boxed{61} \).

---

Would you like more details or have any questions? 

Here are 5 related questions for further practice:

1. What is the common difference if the first term is 10 and the eighth term is 50?
2. How many terms are in an arithmetic sequence if the first term is 2, the last term is 50, and the common difference is 4?
3. Determine the sum of the first 20 terms of an arithmetic sequence with a first term of 3 and a common difference of 5.
4. If the fifth term of an arithmetic sequence is 25 and the tenth term is 50, what is the common difference?
5. Find the 25th term of an arithmetic sequence if the first term is 7 and the common difference is 3.

**Tip**: Always start by identifying key information such as the first term and common difference in an arithmetic sequence problem.

Determine the fifteenth term of the arithmetic sequence in which the first term is 5 and the eighth term is 33.

Discover how to find the 15th term of an arithmetic sequence where the first term is 5 and the eighth term is 33. This step-by-step solution explains how to calculate the common difference and use the general term formula. Perfect for students in Grades 8-10.

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