Pattern Completion Notes & Questions | Class 5 Reasoning | Drishti OS

Pattern Completion

What you will learn

How to find the repeating cycle in a pattern of shapes, sizes, or numbers.
How to complete a number grid where each row or column follows a fixed rule (like a constant sum).
A step-by-step method: find the cycle length, count how far along the cycle you are, then predict the next item.

Key concepts

Level 1 — Repeating shape cycles

Verbal: A short group of shapes repeats again and again, in the same order.

Symbolic: Circle, Square, Triangle, Circle, Square, ? — cycle length 3, so next is Triangle.

Pattern	Cycle length	Next item
Square, Triangle, Circle, Square, Triangle, ?	3	Circle
Big, Small, Big, Small, ?	2	Big

Level 2 — Two features combined

Verbal: When two properties (like size and shape) each repeat on their own cycle, the combined pattern repeats after the smallest number that both cycles divide into evenly (their LCM).

Real-life: A tiled floor pattern that alternates both color and shape.

Level 3 — Number grids

Verbal: In some grids, every row (or column) of numbers adds up to the same total. Use that total to find a missing number.

Worked example

Pattern: Big Circle, Small Square, Big Triangle, Small Circle, Big Square, ? Find the next term.

Step 1 - Shape cycles every 3: Circle, Square, Triangle, Circle, Square, Triangle...
Step 2 - Size cycles every 2: Big, Small, Big, Small, Big, Small...
Step 3 - Combined cycle repeats every 6 terms
Step 4 - The 6th term (matching position 6) is Small Triangle
Answer: Small Triangle

Row of numbers 5, 7, x adds to 16. Find x.

Step 1 - Row sum is 16
Step 2 - x = 16 - 5 - 7 = 4
Answer: 4

Common mistakes

Mistake	Why it happens	Fix
Wrong cycle length	Not checking enough terms	Write out at least 2 full cycles before deciding
Ignoring one of two properties	Focusing only on shape, not size (or vice versa)	Track each property in its own row
Adding row wrong	Arithmetic slip	Re-add the known numbers before subtracting
Assuming column rule instead of row rule	Misreading the question	Re-read whether the rule applies to rows or columns

Quick check

What comes after Circle, Triangle, Square, Circle, Triangle?
If a row of 3, 6, x sums to 12, what is x?
What is the cycle length if Big/Small repeats every 2 and Red/Blue/Green repeats every 3?
Stretch: List all 6 terms of a Big/Small + Circle/Square/Triangle combined cycle starting at Small Square.

Revision tip: For grid questions, always add the known numbers first, then subtract from the total.

Open the Practice tab for graded questions on Pattern Completion.

Pattern Completion