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How many cubes would there be on the 6th pattern

To analyze the image, I observe a series of patterns made from cubes. The sequence involves stacked cube formations, with each pattern increasing the number of cubes as it progresses.

Here is what I can deduce from the image:
- The first pattern contains 2 cubes.
- The second pattern contains 4 cubes.
- The third pattern contains 6 cubes.
- The fourth pattern contains 8 cubes.
- The fifth pattern contains 10 cubes.

It appears that the number of cubes increases by 2 with each subsequent pattern. This suggests an arithmetic progression where the number of cubes in the \(n\)-th pattern is given by the formula:

\[
C(n) = 2n
\]

Thus, for the 6th pattern, the number of cubes will be:

\[
C(6) = 2 \times 6 = 12
\]

So, there would be **12 cubes** in the 6th pattern.

Would you like more details on how arithmetic progressions work, or do you have any other questions?

Here are some related questions you might be interested in:
1. What is an arithmetic sequence?
2. How can we find the general term of an arithmetic progression?
3. What are some real-world examples of arithmetic sequences?
4. Can the difference between terms in a sequence be negative?
5. How can we calculate the sum of the first \(n\) terms in an arithmetic sequence?

**Tip:** When recognizing patterns, look for a constant rate of change between consecutive terms—this is often a sign of an arithmetic sequence.

How many cubes would there be on the 6th pattern?

Learn how to determine the number of cubes in the 6th pattern using an arithmetic sequence. The problem involves recognizing a pattern where the number of cubes increases by 2 in each step. Suitable for students in Grades 5-7.

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