The numbers you provided (4, 9, and 16) follow a pattern related to squares of integers. Specifically, each of these numbers is a perfect square:

- \(4 = 2^2\)
- \(9 = 3^2\)
- \(16 = 4^2\)

The general formula to generate these numbers can be expressed as:

\[
n^2
\]

Where \(n\) is any integer. For the given sequence:

- For \(n = 2\), \( n^2 = 4 \)
- For \(n = 3\), \( n^2 = 9 \)
- For \(n = 4\), \( n^2 = 16 \)

Thus, the formula to generate this sequence is \(n^2\), where \(n\) is a positive integer starting from 2.

Would you like further details or have any questions?

Here are 5 related questions to consider:
1. How would you find the next number in this sequence?
2. What would the pattern look like if you squared negative numbers?
3. How does this formula relate to geometric shapes?
4. Can you apply this formula to non-integer values?
5. How do perfect squares relate to quadratic equations?

**Tip:** Recognizing common patterns like squares in number sequences can help in identifying and solving many types of mathematical problems quickly.

Learn how to derive a formula for the numbers 4, 9, and 16 by recognizing the pattern of perfect squares. This page explains the formula n^2, where n is a positive integer, with detailed examples and related concepts. Suitable for students in Grades 6-8.

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