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The problem in the image asks to find the 100th term of the sequence 6, 12, 18, ...

This sequence appears to be an **arithmetic sequence**, where each term increases by a constant value. Let's analyze it:

1. **First term (a)** = 6
2. **Common difference (d)** = 12 - 6 = 6

The formula for the \(n\)-th term of an arithmetic sequence is:

\[
a_n = a + (n - 1) \cdot d
\]

Substituting the values for the 100th term:

\[
a_{100} = 6 + (100 - 1) \cdot 6
\]

Now, I will calculate this.

The 100th term of the sequence is \( 600 \).

Would you like more details or have any other questions?

Here are some related questions:
1. How do you find the sum of the first 100 terms of this arithmetic sequence?
2. What would the 50th term of the same sequence be?
3. How do you know if a sequence is arithmetic or geometric?
4. How can you calculate the general formula for any term in an arithmetic sequence?
5. Can an arithmetic sequence have a common difference of zero?

**Tip**: In arithmetic sequences, the difference between consecutive terms is always constant. Identifying this difference is key to solving related problems efficiently.

Find the 100th term of the following sequence: 6, 12, 18, ...

Discover how to find the 100th term of the arithmetic sequence starting with 6, 12, 18. This solution includes a step-by-step explanation using the formula for the nth term of an arithmetic sequence. Suitable for students in Grades 7-10.

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