COMPLETE THE PATTERN

A structured approach to identifying and extending sequences, grids, and logical patterns. Use observation, rule deduction, and verification to reliably complete the next steps.

Concept

Patterns emerge from consistent rules governing progression, repetition, or transformation. By isolating the rule, you can predict the missing element or the next stage with confidence.

Step-by-step approach

1. Observe the given sequence or pattern carefully.
2. Identify changes between terms: increments, reductions, alternations, or transformations.
3. Test potential rules on multiple parts of the pattern.
4. Apply the rule to determine the missing element.
5. Verify by back-checking with the existing terms.

Practice exercises

• Sequence: 2, 4, 6, 8, __
  • Next term: 10
• Sequence: A, C, E, G, __
  • Next term: I
• Pattern with alternation: 1, 4, 2, 5, 3, 6, __
  • Next term: 4
• Pattern with doubling and addition: 3, 6, 12, 24, __
  • Next term: 48
• Grid-based pattern (row-wise):
  • Row 1: 1, 2, 3
  • Row 2: 4, 5, 6
  • Row 3: 7, 8, 9
  • What comes next in the sequence if continuing row-major order?
  • Next term: 10

Tips for mastering pattern completion

• Write out terms and look for the smallest repeating unit.
• Consider multiple rules (arithmetic, geometric, positional, or digital operations).
• Check edge cases where patterns may shift or reset.
• Use diagrams or simple sketches to visualize grids or sequences.

Challenge questions

• Create a sequence of length six where the rule changes after the third term. Explain the rule for the first three terms and the rule for the last three.
• Design a two-dimensional pattern in a 3×3 grid where each row follows a distinct rule but the entire grid shares a unifying concept. Provide the completed grid.