About Number Patterns & Puzzles — Class 7 CBSE

Recognize, describe, and extend number patterns and solve number puzzles. This topic is part of the CBSE Class 7 mathematics syllabus (chapter: Chapter 6). On this page you can practice 60 questions across three difficulty levels — 20 easy, 20 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 35-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

What you'll learn in Number Patterns & Puzzles

• Introduction to Number Patterns
• Uncovering the Rules of Patterns
• Introduction to Magic Squares
• Exploring Special Number Patterns
• Creating Your Own Patterns and Puzzles

Interactive lesson · about 15 minutes · checkpoint question after every unit

Number Patterns & Puzzles — solved examples for Class 7 CBSE

Practice questions on Number Patterns & Puzzles

1. Q1.easy

   Observe the pattern: 1, 4, 7, 10, ... Which of the following statements correctly describes the rule for this pattern?

   1. A)Start with 1 and add 4 to the previous number.
   2. B)Start with 1 and subtract 3 from the previous number.
   3. C)Start with 1 and add 3 to the previous number.
   4. D)Start with 1 and multiply by 3 each time.
   Show answer

   Answer: Start with 1 and add 3 to the previous number.

   Hint: Check the difference between successive terms to find the operation.

2. Q2.easy

   A 3×3 magic square has numbers arranged such that the sum of the numbers in each row, each column, and both main diagonals is the same. This constant sum is called the magic constant. If a 3×3 square has a magic constant of 15, which of the following statements must be true?

   1. A)The sum of all numbers in the square is 15.
   2. B)All numbers in the square must be prime numbers.
   3. C)The number in the center cell must be 5.
   4. D)The square must contain only even numbers.
   Show answer

   Answer: The number in the center cell must be 5.

   Hint: For a 3x3 magic square, the middle number has a special relationship with the magic constant.

3. Q3.easy

   Consider a 3×3 magic square where the magic constant is 24. If one row has the numbers 7, ___, 13, what is the missing number?

   1. A)4
   2. B)8
   3. C)10
   4. D)12
   Show answer

   Answer: 4

   Hint: The sum of numbers in any row of a magic square must equal the magic constant.

4. Q4.medium

   Identify the missing number in the sequence: 3, 9, 27, ___, 243.

   1. A)54
   2. B)81
   3. C)108
   4. D)135
   Show answer

   Answer: 81

   Hint: Consider if each term is obtained by multiplying the previous term by a constant factor.

5. Q5.medium

   Consider a sequence where the first two terms are 1 and 3. Each subsequent term is the sum of the two preceding terms. What is the 5th term in this sequence?

   1. A)7
   2. B)10
   3. C)11
   4. D)13
   Show answer

   Answer: 11

   Hint: Write down the terms step-by-step, adding the previous two numbers each time.

6. Q6.medium

   A 3×3 magic square has the sum of numbers in each row, column, and main diagonal equal to 15. If the square is:
   8 ? 6
   3 5 7
   4 9 2
   What number should replace '?' to complete the magic square?

   1. A)1
   2. B)10
   3. C)15
   4. D)1
   Show answer

   Answer: 1

   Hint: Use the property that the sum of numbers in any row, column, or main diagonal must be 15.

7. Q7.hard

   Consider a sequence where the first term is 4. Each subsequent term is found by first multiplying the previous term by 2, and then subtracting 1. What is the sum of the 3rd, 4th, and 5th terms of this sequence?

   1. A)78
   2. B)81
   3. C)84
   4. D)87
   Show answer

   Answer: 87

   Hint: Carefully calculate the first few terms of the sequence step-by-step using the given rule. Once you have the 3rd, 4th, and 5th terms, sum them up.

8. Q8.hard

   In a special number sequence, the first term is 3, and the second term is 5. From the third term onwards, each term is obtained by adding the two previous terms and then subtracting 1. What is the 7th term of this sequence?

   1. A)43
   2. B)55
   3. C)67
   4. D)79
   Show answer

   Answer: 43

   Hint: Write down the recurrence relation carefully. Calculate the terms one by one, ensuring you apply both addition and subtraction steps correctly for each new term.

9. Q9.hard

   Consider a pattern of solid squares formed by smaller unit squares. Figure 1 is a 1×1 solid square. Figure 2 is a 2×2 solid square. Figure 3 is a 3×3 solid square. If each Figure N is then modified by adding a border of unit squares, 1 unit thick, around its entire perimeter, what will be the total number of unit squares in the modified Figure 5?

   1. A)36
   2. B)42
   3. C)49
   4. D)56
   Show answer

   Answer: 49

   Hint: For a Figure N (an N×N square), think about how adding a 1-unit thick border changes its overall dimensions (length and width). This will help you find the total number of squares in the new, larger square.

These are 9 of the 60 questions available for Number Patterns & Puzzles. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.