Find the 60th term of the arithmetic sequence minus, 27, comma, minus, 24, comma, minus, 21, comma, point, point, .−27,−24,−21

To find the 60th term of the arithmetic sequence \( -27, -24, -21, \dots \), we will use the formula for the \( n \)-th 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 of the sequence.
- \( d \) is the common difference.
- \( n \) is the term number we want to find.

### Step 1: Identify the first term \( a_1 \)
The first term \( a_1 = -27 \).

### Step 2: Find the common difference \( d \)
The common difference \( d \) is the difference between consecutive terms:
\[
d = -24 - (-27) = 3
\]

### Step 3: Apply the formula for the 60th term
We are looking for the 60th term, so \( n = 60 \). Using the formula:

\[
a_{60} = -27 + (60 - 1) \cdot 3
\]

\[
a_{60} = -27 + 59 \cdot 3
\]

\[
a_{60} = -27 + 177 = 150
\]

### Final Answer:
The 60th term of the sequence is \( 150 \).

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Do you need more details or have any questions?

Here are 5 related questions to explore:
1. What is the general formula for the \( n \)-th term of this arithmetic sequence?
2. How would you find the sum of the first 60 terms of this sequence?
3. How do you determine if a sequence is arithmetic?
4. Can you derive the 100th term of this sequence?
5. What is the significance of the common difference in an arithmetic sequence?

**Tip:** Always verify the common difference by checking between a few consecutive terms in the sequence!

Find the 60th term of the arithmetic sequence −27,−24,−21,...

Learn how to find the 60th term of the arithmetic sequence −27,−24,−21,... using the formula a_n = a_1 + (n - 1) * d. This problem focuses on arithmetic sequences and algebra, suitable for students in Grades 6-8.

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