Patterns in Mathematics Sums for Class 6 — Free CBSE Worksheet PDF with Answers

Patterns are the heart of mathematics. The times table is a pattern. The way odd numbers add up to make perfect squares is a pattern. Even the spiral of a sunflower follows a mathematical rule. In Class 6 CBSE, the Patterns in Mathematics chapter introduces you to recognising and extending patterns in numbers and shapes — the skill that later helps you write algebraic rules and crack competitive exam problems.

This chapter covers number sequences, shape patterns, triangular and square numbers, sums of odd numbers, matchstick patterns, and writing the rule for the $n$-th term. The chapter exercise expects students to find the next term, find the rule, and explain why the rule works.

The worksheet has 60 questions across three levels. Level 1 covers identifying the next term and simple patterns. Level 2 works on finding rules, triangular and square numbers, and matchstick patterns. Level 3 asks students to write general rules for the $n$-th term and reason about multi-step patterns.

Triangular numbers can form an equilateral triangle of dots: $1, 3, 6, 10, 15, 21, \ldots$. Each new term adds one more row. The $n$-th triangular number is $\frac{n(n+1)}{2}$. So the 6th triangular number is $\frac{6 \times 7}{2} = 21$. The differences between consecutive triangular numbers are $1, 2, 3, 4, 5, \ldots$ — they grow by one each time.

Square numbers form a square arrangement of dots: $1, 4, 9, 16, 25, \ldots$. The $n$-th square number is $n^2$. There is a beautiful connection: the sum of the first $n$ odd numbers is $n^2$. So $1 = 1^2$, $1 + 3 = 4 = 2^2$, $1 + 3 + 5 = 9 = 3^2$, $1 + 3 + 5 + 7 + 9 + 11 = 36 = 6^2$. This pattern is exam favourite material.

Look at the differences between consecutive terms first. If the differences are constant (like $4, 4, 4$), the pattern is arithmetic, and the rule has the form $4n + c$ for some constant $c$. To find $c$, plug in $n = 1$ and use the first term.

Example: pattern is $5, 8, 11, 14, \ldots$. Differences are $3, 3, 3$, so rule is $3n + c$. When $n = 1$, value is $5$, so $3(1) + c = 5$, giving $c = 2$. Rule: $3n + 2$. Check: $n = 4$ gives $3(4) + 2 = 14$. Correct. So the 20th term is $3(20) + 2 = 62$.

If the differences themselves form a pattern (like $1, 2, 3, 4$), the pattern is more complex. Triangular numbers behave this way. The rule may involve $n^2$ or other forms — Class 6 students typically only need to find rules for arithmetic patterns and recognise the famous sequences.

Matchstick patterns are a classic introduction to algebra. To make 1 square in a row uses 4 matchsticks. To make 2 squares (sharing one side) uses 7 matchsticks. To make 3 squares uses 10 matchsticks. The pattern is $4, 7, 10, \ldots$ with constant difference $3$, so the rule is $3n + 1$.

Dot triangle patterns: row 1 has 1 dot, row 2 has 2 dots, row 3 has 3 dots, and so on. The total dots after $n$ rows is the $n$-th triangular number. After 8 rows: $\frac{8 \times 9}{2} = 36$ dots. Recognising these classic shape-to-number connections is a major skill in Class 6.