Mathematics July 22, 2026 · 10 min read

Number Sequences: Finding Patterns in Mathematics

Analyze number sequences to find patterns, identify types, and compute terms. Learn to recognize arithmetic, geometric, and quadratic sequences.

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Number sequences are ordered lists of numbers following specific patterns. Recognizing these patterns is fundamental to mathematics, enabling prediction, generalization, and deeper understanding of numerical relationships.

Types of Sequences

  • Arithmetic: Constant difference between terms (2, 5, 8, 11, ...)
  • Geometric: Constant ratio between terms (3, 12, 48, 192, ...)
  • Quadratic: Constant second differences (1, 4, 9, 16, 25, ...)
  • Fibonacci: Each term is the sum of the two preceding (0, 1, 1, 2, 3, 5, ...)

How to Identify Patterns

  1. Check differences: If constant — arithmetic
  2. Check ratios: If constant — geometric
  3. Check second differences: If constant — quadratic
  4. Look for known sequences: Fibonacci, primes, powers

Worked Example

Analyze: 2, 5, 8, 11, 14, ...

  1. Differences: 3, 3, 3, 3 (constant)
  2. Arithmetic sequence with d = 3
  3. Formula: aₙ = 2 + (n-1)(3) = 3n - 1
  4. Next terms: 17, 20, 23