CBSE Class 6 Maths (Ganita Prakash) Important Questions Chapter 3 - Number Play

1. What is the sum of the first 10 natural numbers?  

Ans:  \[S = \frac{n(n + 1)}{2} = \frac{10(10 + 1)}{2} = \frac{10 \times 11}{2}\]= 55

2. If a number is increased by 8 and the result is 15, what is the number?  

Ans: Let the number be x.  

x + 8 = 15

x = 15 - 8 = 7 

3. What is the 5th term in the sequence 2, 4, 6, 8, ...?  

Ans: The sequence is an arithmetic progression where the first term a = 2 and the common difference d = 2 

The nth term is given by $ a_n = a + (n-1)d $.  

So, $ a_5$ = 2 + (5-1) $\times $2 = 2 + 8 = 10 .

4. What is the sum of the first 5 odd numbers?  

Ans: The first 5 odd numbers are 1, 3, 5, 7, and 9.  

Sum =  1 + 3 + 5 + 7 + 9 = 25   

Alternatively, S = $n^{2}$ = $5^{2}$ = 25).

5. What is the sum of the first 4 even numbers?  

Ans: The first 4 even numbers are 2, 4, 6, and 8.  

Sum = 2 + 4 + 6 + 8 = 20 

Alternatively, S = n(n + 1) = 4 $\times $5 = 20.

6. If the 3rd term of an arithmetic sequence is 12 and the common difference is 4, what is the first term?  

Ans: Let the first term be a

The 3rd term is a + 2d = 12 

So,  a + 2 $\times $4 = 12 

a + 8 = 12  

a = 12 - 8 = 4.

7. How many numbers are there between 1 and 100 that are multiples of 5?  

Ans: The multiples of 5 from 1 to 100 are 5, 10, 15, ..., 100.  

This is an arithmetic sequence where a = 5 , d = 5, and $a_n $= 100 

n = $\dfrac{100 - 5}{5} $+ 1 = 20 . There are 20 multiples of 5.

8. If the 4th term of a sequence is 20 and the common difference is 3, what is the 1st term?  

Ans: Let the first term be a 

The 4th term is a + 3d = 20 

So, a + 3 $\times $3 = 20 

a + 9 = 20 

a = 20 - 9 = 11 

9. Find the sum of the first 6 squares of natural numbers.  

Ans: The squares of the first 6 natural numbers are $1^{2}, 2^{2}, 3^{2}, 4^{2}, 5^{2}, 6^{2} $.  

Sum = 1 + 4 + 9 + 16 + 25 + 36 = 91 

Alternatively, using the formula S = $\dfrac{n(n + 1)(2n + 1)}{6} $

S =$ \dfrac{6(6 + 1)(2 \times 6 + 1)}{6} $= $\dfrac{6 \times 7 \times 13}{6} $= 91

10. What is the 7th term in the sequence: 5, 10, 15, 20, ...?  

Ans: This sequence has a first term a = 5 and a common difference d = 5

The 7th term is given by $a_n $= a + (n - 1)d 

So, $a_7 $= 5 + (7 - 1) $\times $5 = 5 + 30 = 35 

11. What is the sum of the first 15 natural numbers?  

Ans: S = $\dfrac{n(n + 1)}{2}$ = $\dfrac{15(15 + 1)}{2} $= $\dfrac{15 \times 16}{2} $= 120 

12. If a number is decreased by 4 and the result is 9, what is the number?  

Ans: Let the number be x 

x - 4 = 9 

x = 9 + 4 = 13 

13. What is the 6th term in the sequence 3, 6, 9, 12, ...?  

Ans: The sequence is an arithmetic progression where a = 3 and d = 3 

The 6th term is $a_6$ = a + (6 - 1)d = 3 + 15 = 18 

14. What is the sum of the first 7 odd numbers?  

Ans: The first 7 odd numbers are 1, 3, 5, 7, 9, 11, and 13.  

Sum = 1 + 3 + 5 + 7 + 9 + 11 + 13 = 49 

Alternatively, S =$ n^{2} $= $7^{2}$= 49).

15. What is the sum of the first 10 even numbers?  

Ans: The first 10 even numbers are 2, 4, 6, ..., 20.  

Sum = 2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 = 110 

Alternatively, S = n(n + 1) = 10 $\times $11 = 110

16. If the 2nd term of an arithmetic sequence is 8 and the common difference is 3, what is the first term?  

Ans: Let the first term be a 

The 2nd term is a + d = 8 

So, a + 3 = 8 

a = 8 - 3 = 5 

17. How many numbers are there between 1 and 50 that are multiples of 10?  

Ans: The multiples of 10 from 1 to 50 are 10, 20, 30, 40, and 50.  

This forms an arithmetic sequence where a = 10, d = 10 

There are n =$ \dfrac{50 - 10}{10} $+ 1 = 5 multiples of 10.

18. If the 5th term of a sequence is 25 and the common difference is 5, what is the 1st term?  

Ans: Let the first term be a.  

The 5th term is a + 4d = 25   

So, a + 4 $\times $5 = 25 

a + 20 = 25 

a = 25 - 20 = 5 

19. Find the sum of the first 8 squares of natural numbers.  

Ans: The squares of the first 8 natural numbers are $1^{2}, 2^{2}, 3^{2}, 4^{2}, 5^{2}, 6^{2}, 7^{2}, 8^{2}$.  

Sum = 1 + 4 + 9 + 16 + 25 + 36 + 49 + 64 = 204 

Alternatively, using the formula S = $\dfrac{n(n + 1)(2n + 1)}{6} $:  

S =$ \dfrac{8(8 + 1)(2 \times 8 + 1)}{6}$ = 204.

20. What is the 9th term in the sequence: 4, 8, 12, 16, ...?  

Ans: The sequence has a first term a = 4 and a common difference d = 4.  

The 9th term is given by $a_9$ = a + (9 - 1)d .  

So, $ a_9$ = 4 + (8 $\times$ 4) = 4 + 32 = 36 

5 Important Formulas of Class 6 Chapter 3 You Shouldn’t Miss!

Benefits of Class 6 Maths Important Questions Chapter 3 Number Play

• Improves Learning: Important questions help students revisit key concepts from "Number Play," such as patterns and sequences, reinforcing their understanding.

• Enhances Problem-Solving Skills: Working through these questions improves critical thinking and problem-solving abilities, making maths more enjoyable and less daunting.

• Builds Confidence: As students practise and master important questions, they gain confidence in their maths skills, which can lead to better performance in exams.

• Exam Preparation: These questions are aligned with the CBSE Class 6 syllabus, ensuring students are well-prepared for their assessments and understand what to expect.

• Identifies Weak Areas: By tackling a variety of important questions, students can identify areas where they may need more practice or help, allowing for focused learning.

• Encourages Active Learning: Engaging with important questions promotes active learning, encouraging students to think independently and apply what they’ve learned in real-life situations.

Conclusion 

Vedantu's important questions for Class 6 Maths Chapter 3 Number Play provide a valuable resource for students. They not only cover essential topics like patterns and sequences but also encourage students to think critically and solve problems effectively. By practising these questions, learners can strengthen their understanding and build confidence in their maths skills. This approach makes learning enjoyable and helps students prepare better for their exams. With a focus on practical application, these important questions guide students toward learning the concepts in a fun and engaging way.

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