Math Problem Statement

What is the next term in the following number pattern?1, 4, 9, 16, 25,

Solution

The given number pattern is:

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

These numbers are the squares of consecutive integers:

  • 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 term would be:

62=366^2 = 36

Thus, the next term in the pattern is 36.

Would you like more details or have any questions?

Here are 5 related questions for practice:

  1. What is the next term after 36 in this pattern?
  2. What is the general formula for the nn-th term of this pattern?
  3. How would you describe the difference between consecutive terms in this sequence?
  4. Can you find the 10th term in this sequence?
  5. How do you find the sum of the first nn square numbers?

Tip: Recognizing patterns like perfect squares can often help you predict future terms quickly in a sequence.

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Math Problem Analysis

Mathematical Concepts

Algebra
Patterns
Perfect Squares

Formulas

n^2 where n is a positive integer

Theorems

Theory of Square Numbers

Suitable Grade Level

Grades 5-7