Math Problem Statement

Find the next two number terms in the sequence of square numbers: 1, 4, 9, 16.

Solution

The given image shows the first four square numbers, which are visualized using squares made of unit blocks. The sequence of the numbers is:

1, 4, 9, 16.

These are the square numbers because they are derived from squaring integers:

  • 12=11^2 = 1,
  • 22=42^2 = 4,
  • 32=93^2 = 9,
  • 42=164^2 = 16.

To find the next two terms in the sequence, we calculate:

  • 52=255^2 = 25,
  • 62=366^2 = 36.

Thus, the next two numbers in the sequence are 25 and 36.

Would you like further explanations or additional help? Here are five follow-up questions for deeper learning:

  1. What are the square numbers up to 12212^2?
  2. How can you use square numbers to solve geometry problems involving squares?
  3. What is the difference between square numbers and cube numbers?
  4. How can you determine if a number is a perfect square?
  5. What patterns can be observed in the differences between consecutive square numbers?

Tip:

The difference between consecutive square numbers increases by 2 each time (e.g., 41=34 - 1 = 3, 94=59 - 4 = 5, 169=716 - 9 = 7). This is because n2(n1)2=2n1n^2 - (n-1)^2 = 2n - 1.

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Math Problem Analysis

Mathematical Concepts

Number Sequences
Square Numbers

Formulas

n^2

Theorems

Properties of Square Numbers

Suitable Grade Level

Grades 5-7