NCERT Solutions Class 6 Maths Chapter 1 Patterns in Mathematics Exercise 1.2

In Class 6 Maths NCERT Solutions, Chapter 1, Patterns in Mathematics, students learn that patterns are not just found in tellings such as numbers, but also in shapes, designs and objects we find in daily life. The chapter creates an opportunity for mathematics being made interesting and accessible, igniting the curiosity of young minds.

NCERT Solutions Class 6 Maths Chapter 1 Patterns in Mathematics Exercise 1.2 often involves patterns that might require a bit more deduction to uncover the underlying rule, or it could introduce patterns that involve more than one operation or element. By engaging with these problems, students refine their analytical capabilities, becoming more adept at spotting intricate relationships and extending patterns accurately, which is a vital skill for higher-level mathematics and problem-solving in general.

1.0Download NCERT Solutions of Class 6 Maths Chapter 1 Patterns in Mathematics Exercise 1.2: Free PDF

You can download NCERT Solutions for Class 6 Maths Chapter 1, Exercise 1.2 as a free PDF to further improve your skills in problem-solving math questions, and prepare for examinations. 

Key Concepts of Exercise 1.2

• Recognizing repeating patterns and growing patterns in numbers and shapes.
• Understanding how to predict the next patterns in a sequence.
• Learning patterns as they relate to multiplication tables and arithmetic.
• Learning to create and extend patterns based on rules.
• Using pattern knowledge as it supports real world examples.

2.0NCERT Exercise Solutions Class 6 Chapter 1- Patterns in Mathematics : All Exercises 

3.0NCERT Class 6 Chapter 1 Patterns in Mathematics Exercise 1.2 : Detailed Solutions

1.2 Patterns In Numbers

1. Can you recognize the pattern in each of the sequences given below? 1, 1, 1, 1, 1, 1, 1, ..... 1, 2, 3, 4, 5, 6, 7, ..... 1, 3, 5, 7, 9, 11, 13, ..... 2, 4, 6, 8, 10, 12, 14, ..... $1,3,6,10,15,21,28,\dots .$. 1, 4, 9, 16, 25, 36, 49, ..... 1, 8, 27, 64, 125, 216, ..... 1, 2, 3, 5, 8, 13, 21, ..... 1, 2, 4, 8, 16, 32, 64, ..... 1, 3, 9, 27, 81, 243, 729, ... Sol. Examples of number sequences

Sol. Next three numbers in each sequence:

• All 1's: 1, 1, 1 In the sequence, Sequence of all 1 's.
• Counting numbers: $1,2,3,4,5,6,7,8,9,10$ In the sequence, A sequence of consecutive counting numbers starting from 1, adding 1 to the previous term to get the next term, as $1,1+1=2,2+1=3,3+1=4\dots .$.
• Odd numbers: $1,3,5,7,9,11,13,15,17,19$ In the sequence, A sequence of consecutive odd numbers starting from 1, adding 2 to the previous term to get the next term, as $1,1+2=3,3+2=5,5+2=7,7+2=9\dots$
• Even numbers: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 In the sequence, A sequence of consecutive even numbers starting from 2 , adding 2 to the previous term to get the next term, as $2,2+2=4,4+2=6,6+2=8,8+2=10\dots$
• Triangular numbers: $1,3,6,10,15,21,28,36,45,55$ In the sequence, each term is the sum of first $n$ consecutive counting numbers, as $1=1$, $1+2=3,1+2+3=6,1+2+3+4=10,1+2+3+4+5=15,1+2+3+4+5+6=21$.
• Squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 In the sequence, each term is the product of counting number by itself starting from 1 , as $1\times 1=1,2\times 2=4,3\times 3=9,4\times 4=16,5\times 5=25\dots$
• Cubes: 1, 8, 27, 64, 125, 216, 343, 512, 729 In the sequence, each term is the product of counting number by itself thrice starting from 1 , as $1\times 1\times 1=1,2\times 2\times 2=8,3\times 3\times 3=27,4\times 4\times 4=64,5\times 5\times 5=125$, $6\times 6\times 6=216\dots$
• Virahānka numbers : 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 In the sequence, each term (starting from third term) is the sum of previous two terms.
• Powers of 2: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512 In the sequence, next term is the double of previous term, as $1,1\times 2=2,2\times 2=4$, $4\times 2=8,8\times 2=16,16\times 2=32$
• Powers of 3: 1, 3, 9, 27,81, 243,729, 2187, 6561, 19683 In the sequence, next term is the thrice of previous term, as $1,1\times 3=3,3\times 3=9,9\times 3=27$, $27\times 3=81,81\times 3=243,243\times 3=729$.

4.0Key Features and Benefits Class 6 Maths Chapter 1 Patterns in Mathematics: Exercise 1.2

• Promotes more in-depth logical thinking and observational skills. 
• Engages with real-world examples of patterns, making learning enjoyable and interactive. 
• Provides a basis for confidence when tackling more advanced topics like sequences and algebra.
• Detailed solutions provide conceptual clarity to seemingly complex patterns. 
• Develops invaluable problem-solving skills that can be used in school and the real world.