Math Problem Statement

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

Solution

The given sequence is:

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

This is a sequence of perfect squares:

  • 1=121 = 1^2
  • 4=224 = 2^2
  • 9=329 = 3^2
  • 16=4216 = 4^2
  • 25=5225 = 5^2

Following this pattern, the next number in the sequence is 62=366^2 = 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 nnth 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.

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Math Problem Analysis

Mathematical Concepts

Sequences
Perfect Squares

Formulas

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Theorems

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Suitable Grade Level

Grades 6-8