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!