What number comes next in the following sequence? 1 4 9 16 25...

The given sequence is:

\[ 1, 4, 9, 16, 25, \dots \]

This is a sequence of perfect squares:

- \(1 = 1^2\)
- \(4 = 2^2\)
- \(9 = 3^2\)
- \(16 = 4^2\)
- \(25 = 5^2\)

Following this pattern, the next number in the sequence is \(6^2 = 36\).

So, the next number is **36**.

Would you like more details on this sequence, or have any other questions?

Here are 8 related questions to explore:

1. What is the general formula for the \(n\)th term in this sequence?
2. How would you find the 10th term in this sequence?
3. Can you identify other sequences involving square numbers?
4. What is the difference between successive terms in this sequence?
5. How can you represent this sequence graphically?
6. What are triangular numbers, and how do they relate to square numbers?
7. Can square numbers be written as a sum of consecutive odd numbers?
8. How does this sequence relate to the Pythagorean theorem?

**Tip:** Perfect squares often appear in geometry, such as when calculating the area of a square-shaped region.

Discover how to find the next number in the sequence 1 4 9 16 25... which follows a pattern of perfect squares. Learn about sequences and perfect squares with a step-by-step explanation. Suitable for students in Grades 6-8.

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