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Patterns in Mathematics – Class 6 Mathematics notes, important questions and MCQs

NCERT Class 6 Mathematics, chapter 1. Notes, key terms, important questions with answers and MCQs.

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Chapter overview

Mathematics is the study of patterns. Number sequences and shape patterns follow rules we can discover and extend.

Number patterns

  • Counting numbers 1, 2, 3…; odd numbers 1, 3, 5…; even numbers 2, 4, 6….
  • Square numbers 1, 4, 9, 16…; triangular numbers 1, 3, 6, 10…; cube numbers 1, 8, 27….
  • Powers of 2: 1, 2, 4, 8, 16….

Seeing patterns

  • Adding odd numbers gives squares: 1 + 3 + 5 = 9.
  • Shapes can show number patterns (dots arranged in triangles or squares).
  • Find the rule, then use it to predict the next terms.

Key terms

Sequence
numbers in a definite order following a rule
Square number
a number like n × n
Triangular number
number of dots that form a triangle: 1, 3, 6, 10…

Formulas

  • 1 + 3 + 5 + … (n odd numbers) = n²

Important questions with answers

Write the first five square numbers and the first five triangular numbers.2 marks

Square numbers: 1, 4, 9, 16, 25. Triangular numbers: 1, 3, 6, 10, 15.

Find the sum 1 + 3 + 5 + 7 + 9 + 11 + 13 without adding one by one.3 marks

These are the first 7 odd numbers, and the sum of the first n odd numbers is n². So the sum = 7² = 49.

Look at the pattern 1, 1 + 2 + 1, 1 + 2 + 3 + 2 + 1, … Find the value of each of the first four terms. What do you notice, and what will 1 + 2 + … + 10 + … + 2 + 1 equal?5 marks

1 = 1; 1 + 2 + 1 = 4; 1 + 2 + 3 + 2 + 1 = 9; 1 + 2 + 3 + 4 + 3 + 2 + 1 = 16. The values are square numbers: going up to n and back gives n². So 1 + 2 + … + 10 + … + 2 + 1 = 10² = 100.

Quick revision

  • Odd numbers add up to squares.
  • Triangular numbers: 1, 3, 6, 10, 15.
  • Powers of 2 double each time.

Exam tips

  • Look at differences between terms to spot the rule.
  • Draw dots to understand triangular and square numbers.

Practice MCQs

  1. Next number in 2, 4, 6, 8, … is

    1. 9
    2. 10
    3. 12
    4. 16
    Show answer

    Answer: (b) 10. Add 2.

  2. Which is a square number?

    1. 12
    2. 15
    3. 16
    4. 18
    Show answer

    Answer: (c) 16. 4 × 4.

  3. Next triangular number after 1, 3, 6, 10 is

    1. 13
    2. 14
    3. 15
    4. 16
    Show answer

    Answer: (c) 15. Add 5.

  4. 1 + 3 + 5 + 7 + 9 equals

    1. 20
    2. 30
    3. 24
    4. 25
    Show answer

    Answer: (d) 25. Five odd numbers: 5².

  5. The 6th triangular number is

    1. 21
    2. 15
    3. 28
    4. 18
    Show answer

    Answer: (a) 21. 1 + 2 + 3 + 4 + 5 + 6.

  6. Next number in 1, 2, 4, 8, 16, … is

    1. 32
    2. 24
    3. 20
    4. 18
    Show answer

    Answer: (a) 32. Double each time.

  7. The 10th odd number is

    1. 20
    2. 21
    3. 19
    4. 17
    Show answer

    Answer: (c) 19. 2 × 10 − 1.

  8. The sum of the first 10 odd numbers is

    1. 50
    2. 110
    3. 90
    4. 100
    Show answer

    Answer: (d) 100. Sum of first n odd numbers = n².

All chapters of Class 6 Mathematics

Written by Kundali IQ from standard, well-established facts to help with revision. This is not an official NCERT publication; always read your textbook too.