What is the sixth term of the given sequence below?$-60, -49, -38, \cdots$

We are given the sequence: $ -60, -49, -38, \cdots $. To find the sixth term, we need to first determine the pattern in the sequence.

### Step 1: Find the common difference
Let's calculate the difference between consecutive terms:
\[
-49 - (-60) = -49 + 60 = 11
\]
\[
-38 - (-49) = -38 + 49 = 11
\]
The common difference between consecutive terms is $ 11 $.

### Step 2: Use the common difference to find the next terms
The sequence is arithmetic, with a common difference of $ 11 $. To find the sixth term, we will continue adding $ 11 $ to each term.

1. Fourth term:
\[
-38 + 11 = -27
\]
2. Fifth term:
\[
-27 + 11 = -16
\]
3. Sixth term:
\[
-16 + 11 = -5
\]

### Conclusion:
The sixth term of the sequence is $ -5 $.

Would you like to explore how to generalize this to find any term in an arithmetic sequence?

Here are some related questions:
1. How do you find the $n$-th term of an arithmetic sequence?
2. What is the sum of the first $n$ terms of an arithmetic sequence?
3. How can you determine if a sequence is arithmetic or geometric?
4. What are examples of arithmetic sequences in real-world scenarios?
5. How can you solve for the common difference when it is not given directly?

**Tip**: The formula for the $n$-th term of an arithmetic sequence is $ a_n = a_1 + (n-1)d $, where $a_1$ is the first term and $d$ is the common difference.

Discover how to find the sixth term of the arithmetic sequence -60, -49, -38, ... with a detailed step-by-step solution. This problem covers arithmetic sequences, including the formula for the nth term. Suitable for students in Grades 6-8.

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