Class 10 Maths Chapter 5 Arithmetic Progressions MCQs
Are you finding it difficult to remember the formulas and concepts of Chapter 5, ‘Arithmetic Progressions’? Do questions about the nth term and the sum of n terms leave you puzzled? You’ve come to the right place! We are excited to present the Class 10 Maths Chapter 5 Arithmetic Progressions MCQs Quiz. This free online test will help you understand the basic principles of arithmetic progressions and commit their formulas to memory. Let’s give your board exam preparation a strong foundation with this Arithmetic Progressions quiz!
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Arithmetic Progressions MCQs Quiz
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Q1: The list of numbers: 2, 5, 8, 11, … represents what?
A: A Geometric Progression
B: A Harmonic Progression
C: An Arithmetic Progression
D: A Constant Sequence
Explanation: The given list is 2, 5, 8, 11, … Here, each term is 3 more than its previous term (5-2=3, 8-5=3, 11-8=3). Since the common difference is constant, it is an Arithmetic Progression (AP).
Q2: What is the common difference (d) of the Arithmetic Progression (AP): 10, 7, 4, 1, …?
A: -3
B: 3
C: 10
D: 17
Explanation: In an Arithmetic Progression, the common difference (d) = difference between any term and its preceding term. Here, d = 7 – 10 = -3 or d = 4 – 7 = -3 Thus, the common difference is -3.
Q3: What is the formula to find the nth term of an Arithmetic Progression (AP)?
A: \( S_n = \frac{n}{2}[2a + (n-1)d] \)
B: \( a_n = a + (n-1)d \)
C: \( a_n = a + nd \)
D: \( S_n = \frac{n}{2}(a + l) \)
Explanation: In an Arithmetic Progression (AP), the first term is ‘a’ and the common difference is ‘d’. The formula to find the nth term (or general term) is: \( a_n = a + (n-1)d \). This formula helps find any term based on the first term and the common difference.
Q4: What is the 10th term of the Arithmetic Progression (AP): 3, 8, 13, 18, …?
A: 43
B: 48
C: 53
D: 48
Explanation: Given AP: 3, 8, 13, 18, … First term, a = 3 Common difference, d = 8 – 3 = 5 nth term formula: \( a_n = a + (n-1)d \) 10th term, \( a_{10} = 3 + (10-1) \times 5 = 3 + 9 \times 5 = 3 + 45 = 48 \).
Q5: What is the formula to find the sum of the first n terms of an Arithmetic Progression (AP)?
A: \( S_n = a + (n-1)d \)
B: \( S_n = \frac{n}{2}(a + d) \)
C: \( S_n = \frac{n}{2}[2a + (n-1)d] \)
D: \( S_n = n[2a + (n-1)d] \)
Explanation: There are two formulas to find the sum of the first n terms of an AP: 1. \( S_n = \frac{n}{2}[2a + (n-1)d ]\) 2. \( S_n = \frac{n}{2}(a + l) \), where l is the last term. Here, option C is the first formula which uses the first term (a) and the common difference (d).
Q6: What is the sum of the first 12 terms of the Arithmetic Progression (AP): 5, 11, 17, 23, …?
A: 432
B: 420
C: 444
D: 456
Explanation: Given AP: 5, 11, 17, 23, … First term, a = 5 Common difference, d = 11 – 5 = 6 Number of terms, n = 12 Sum formula: \( S_n = \frac{n}{2}[2a + (n-1)d ]\) \( S_{12} = \frac{12}{2}[2 \times 5 + (12-1) \times 6] = 6[10 + 11 \times 6] = 6[10 + 66] = 6 \times 76 = 432 \).
Q7: If the 3rd term of an Arithmetic Progression (AP) is 12 and the 7th term is 24, what is its common difference?
A: 2
B: 3
C: 4
D: 6
Explanation: Let the first term be ‘a’ and the common difference be ‘d’. 3rd term: \( a + 2d = 12 \) …(1) 7th term: \( a + 6d = 24 \) …(2) Subtracting (1) from (2): \( (a+6d) – (a+2d) = 24 – 12 \) \( \Rightarrow 4d = 12 \) \( \Rightarrow d = 3 \). Thus, the common difference is 3.
Q8: The first term of an Arithmetic Progression (AP) is 5 and the common difference is 3. What will be the sum of its first 15 terms?
Q9: What is the sum of all natural numbers from 1 to 100?
A: 5000
B: 5050
C: 5100
D: 5050
Explanation: Natural numbers from 1 to 100 form an AP where a=1, d=1, n=100, l=100. Sum formula: \( S_n = \frac{n}{2}(a + l) \) \( S_{100} = \frac{100}{2}(1 + 100) = 50 \times 101 = 5050 \). This is the famous formula given by Gauss.
Q10: If the 8th term of an Arithmetic Progression (AP) is 37 and the 13th term is 57, what is its common difference?
A: 3
B: 4
C: 5
D: 6
Explanation: Let the first term be ‘a’ and the common difference be ‘d’. 8th term: \( a + 7d = 37 \) …(1) 13th term: \( a + 12d = 57 \) …(2) Subtracting (1) from (2): \( (a+12d) – (a+7d) = 57 – 37 \) \( \Rightarrow 5d = 20 \) \( \Rightarrow d = 4 \). Thus, the common difference is 4.
Q11: The first term of an Arithmetic Progression (AP) is -3 and the common difference is 4. What will be its 20th term?
A: 73
B: 77
C: 81
D: 85
Explanation: Given: a = -3, d = 4, n = 20 nth term formula: \( a_n = a + (n-1)d \) \( a_{20} = -3 + (20-1) \times 4 = -3 + 19 \times 4 = -3 + 76 = 73 \).
Q12: How many terms are there in the Arithmetic Progression (AP): 7, 13, 19, …, 205?
A: 32
B: 33
C: 34
D: 35
Explanation: Given AP: 7, 13, 19, …, 205 First term, a = 7 Common difference, d = 13 – 7 = 6 Last term, l = 205 Let the number of terms be n. nth term formula: \( a_n = a + (n-1)d \) \( 205 = 7 + (n-1) \times 6 \) \( \Rightarrow 205 – 7 = (n-1) \times 6 \) \( \Rightarrow 198 = (n-1) \times 6 \) \( \Rightarrow n-1 = \frac{198}{6} = 33 \) \( \Rightarrow n = 33 + 1 = 34 \). Thus, the number of terms is 34.
Q13: If the sum of the first n terms of an Arithmetic Progression (AP) is \( S_n = 3n^2 + 4n \), then what is its common difference?
A: 3
B: 6
C: 9
D: 12
Explanation: Given: \( S_n = 3n^2 + 4n \) We know that the nth term, \( a_n = S_n – S_{n-1} \) \( S_{n-1} = 3(n-1)^2 + 4(n-1) = 3(n^2 – 2n + 1) + 4n – 4 = 3n^2 – 6n + 3 + 4n – 4 = 3n^2 – 2n – 1 \) Now, \( a_n = S_n – S_{n-1} = (3n^2 + 4n) – (3n^2 – 2n – 1) = 3n^2 + 4n – 3n^2 + 2n + 1 = 6n + 1 \) The nth term is of the form \( a_n = a + (n-1)d \). Comparing with \( a_n = 6n + 1 \), we can write it as \( a_n = 6n + 1 = 7 + (n-1) \times 6 \) (because 6n+1 = 6(n-1)+7). Thus, the common difference, d = 6. Alternatively, d = \( a_2 – a_1 \) \( a_1 = S_1 = 3(1)^2 + 4(1) = 3+4=7 \) \( a_2 = S_2 – S_1 = [3(4)+8] – 7 = (12+8)-7=20-7=13 \) So, d = 13 – 7 = 6.
Q14: What is the sum of the first five multiples of 3?
A: 30
B: 40
C: 45
D: 45
Explanation: First five multiples of 3: 3, 6, 9, 12, 15 This is an AP with a=3, d=3, n=5 Sum formula: \( S_n = \frac{n}{2}[2a + (n-1)d ]\) \( S_5 = \frac{5}{2}[2 \times 3 + (5-1) \times 3] = \frac{5}{2}[6 + 4 \times 3] = \frac{5}{2}[6 + 12] = \frac{5}{2} \times 18 = 5 \times 9 = 45 \). Or, \( S_5 = \frac{5}{2}(a + l) = \frac{5}{2}(3+15) = \frac{5}{2} \times 18 = 45 \).
Q15: The 5th term of an Arithmetic Progression (AP) is 14 and the 10th term is 29. What are its first term and common difference respectively?
A: a=2, d=3
B: a=3, d=2
C: a=4, d=3
D: a=5, d=4
Explanation: Let the first term be ‘a’ and the common difference be ‘d’. 5th term: \( a + 4d = 14 \) …(1) 10th term: \( a + 9d = 29 \) …(2) Subtracting (1) from (2): \( (a+9d) – (a+4d) = 29 – 14 \) \( \Rightarrow 5d = 15 \) \( \Rightarrow d = 3 \) Putting d in (1): \( a + 4 \times 3 = 14 \) \( \Rightarrow a + 12 = 14 \) \( \Rightarrow a = 14 – 12 = 2 \) Thus, the first term is 2 and the common difference is 3.
Quiz Results
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Class 10 Maths Chapter 5 Arithmetic Progressions MCQs
Chapter 5, ‘Arithmetic Progressions,’ focuses on understanding number patterns. In this chapter, you will learn what an Arithmetic Progression (AP) is—a sequence where each term is obtained by adding a fixed number (the common difference) to the preceding term. You will learn the formula for finding the nth term of an AP and the formula for finding the Sum of n terms of an AP. These Arithmetic Progression Formulas are not only useful for your exams but also for solving real-world problems, making them a foundational topic for the CBSE Class 10 Maths Quiz and board exams.
Conclusion
‘Arithmetic Progressions’ is a chapter where you can easily score full marks with the right amount of practice. Our Class 10 Maths Chapter 5 Arithmetic Progressions MCQs Quiz is designed to help you master this important chapter. This quiz gives you repeated practice on key topics like finding the nth term of an AP and the Sum of n terms of an AP. By solving these objective questions, you can improve your speed and accuracy, which is highly beneficial for your Board Exam Preparation. Try this Free Online Maths Quiz for Class 10 now and take your preparation to the next level!
FAQs
1. Question: How many marks from the chapter Arithmetic Progressions are asked in the board exam? Answer: This chapter typically carries 7-8 marks in the CBSE board exam, including MCQs, short answer, and long answer questions.
2. Question: What are the most important formulas in this chapter? Answer: The most important formulas are the formula for the nth term (an = a + (n-1)d) and the formula for the sum of the first n terms (Sn = n/2 [2a + (n-1)d]).
3. Question: Is this Arithmetic Progressions quiz based on the NCERT syllabus? Answer: Yes, our Arithmetic Progressions Class 10 quiz is fully based on the NCERT curriculum and the CBSE syllabus.
4. Question: What is an Arithmetic Progression (AP)? Answer: An Arithmetic Progression is a list of numbers in which each term is obtained by adding a fixed number ‘d’ (the common difference) to its preceding term.
5. Question: How do you find the nth term of an AP? Answer: If the first term is ‘a’ and the common difference is ‘d’, the nth term is given by the formula an = a + (n-1)d.
6. Question: Is this online quiz free? Answer: Yes, this Free Online Maths Quiz for Class 10 is absolutely free. You can take it anytime and anywhere for practice.
7. Question: How should I prepare this chapter for the board exam? Answer: First, memorize all the Arithmetic Progression Formulas well. Then, solve the examples and exercise questions from the NCERT book. Finally, test your knowledge with our Arithmetic Progressions Online Test.
8. Question: How many arithmetic means can be inserted between two numbers? Answer: Any number of arithmetic means can be inserted between two given numbers.
9. Question: How do you find the common difference of an AP? Answer: The common difference can be found by subtracting any term from its succeeding term (d = an – an-1).
10. Question: What is the benefit of taking this online quiz? Answer: This quiz helps you improve time management, check the accuracy of your formulas, and understand the exam pattern, which boosts your confidence and leads to better performance.
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