NCERT Class 7 Maths · Chapter 6
NCERT Solutions Class 7 Maths Chapter 6 — Number Patterns & Puzzles
Step-by-step solutions for all exercises in NCERT Class 7 Maths Number Patterns & Puzzles.
Chapter Overview
Recognize, describe, and extend number patterns and solve number puzzles.
This chapter is part of the NCERT Mathematics textbook for Class 7 and is important for CBSE school examinations. The concepts covered here build the foundation for more advanced topics in higher classes.
Below you will find solved examples from this chapter. Each solution includes detailed step-by-step working so you can understand the method, not just the answer.
Solved Examples from Number Patterns & Puzzles
1What is the next number in the pattern: 3, 7, 11, 15, ___?
Answer: 19
Solution:
Step 1: First, find the difference between consecutive terms: 7 - 3 = 4, 11 - 7 = 4, 15 - 11 = 4.
Step 2: The pattern is to add 4 to the previous term to get the next term.
Step 3: Therefore, the next number in the sequence is 15 + 4 = 19.
2Observe the pattern: 1, 4, 7, 10, ... Which of the following statements correctly describes the rule for this pattern?
Answer: Start with 1 and add 3 to the previous number.
Solution:
Step 1: Compare the first two terms: 4 - 1 = 3.
Step 2: Compare the second and third terms: 7 - 4 = 3.
Step 3: Compare the third and fourth terms: 10 - 7 = 3.
Step 4: The pattern shows a constant addition of 3 to the previous term, starting with 1.
3A 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?
Answer: The number in the center cell must be 5.
Solution:
Step 1: In any 3×3 magic square, the number in the center cell is always equal to the magic constant divided by 3.
Step 2: Given the magic constant is 15.
Step 3: Therefore, the number in the center cell = 15 / 3 = 5.
Step 4: Other options are not necessarily true. For example, the sum of all numbers in a 3x3 magic square with magic constant M is 3M, so it would be 3 × 15 = 45, not 15.
4Consider a 3×3 magic square where the magic constant is 24. If one row has the numbers 7, ___, 13, what is the missing number?
Answer: 4
Solution:
Step 1: The magic constant for this square is 24.
Step 2: In a magic square, the sum of numbers in any row must equal the magic constant.
Step 3: Let the missing number be 'x'. So, for the given row: 7 + x + 13 = 24.
Step 4: Combine the known numbers: 20 + x = 24. Solving for x, we get x = 24 - 20 = 4.
5A sequence starts with 1, 1. Each subsequent number is the sum of the two preceding numbers. What is the 6th term in this sequence?
Answer: 8
Solution:
Step 1: The sequence starts with the 1st term = 1 and the 2nd term = 1.
Step 2: 3rd term = 1st term + 2nd term = 1 + 1 = 2.
Step 3: 4th term = 2nd term + 3rd term = 1 + 2 = 3.
Step 4: 5th term = 3rd term + 4th term = 2 + 3 = 5.
Step 5: 6th term = 4th term + 5th term = 3 + 5 = 8.
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