Hello students, we are providing assertion reason questions for class 10. Assertion Reason questions are the new question format that is introduced in CBSE board. The resources for assertion reason questions are very less. So, to help students we have created chapterwise assertion reason questions for class 10 maths. In this article, you will find assertion reason questions for CBSE Class 10 Maths Chapter 5 Arithmetic Progressions. It is a part of Assertion Reason Questions for CBSE Class 10 Maths Series.
| Chapter | Arithmetic Progressions |
| Type of Questions | Assertion Reason Questions |
| Nature of Questions | Competency Based Questions |
| Board | CBSE |
| Class | 10 |
| Subject | Maths |
| Useful for | Class 10 Studying Students |
| Answers provided | Yes |
| Difficulty level | Mentioned |
| Important Link | Class 10 Maths Chapterwise Assertion Reason |
Assertion Reason Questions on Arithmetic Progressions
Assertion and Reason Questions
Directions: Each of the following questions consists of two statements: an Assertion (A) and a Reason (R). Answer them by selecting the correct option:
(a) Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
(c) Assertion (A) is true, but Reason (R) is false.
(d) Assertion (A) is false, but Reason (R) is true.
Q1. Assertion (A): The $n$th term of an arithmetic progression is given by $a_n=a+(n-1) d$.
Reason (R): In an AP, the difference between any two consecutive terms is constant.
Answer: Option (a) is correct.
Explanation: The nth term formula arises from the constant difference ddd in the sequence. R correctly explains A.
Difficulty Level: Easy
Q2. Assertion (A): The sequence 5, 9, 14, 20 is an arithmetic progression.
Reason (R): The difference between the terms is not the same throughout.
Answer: Option (c) is correct.
Explanation: Differences are 4, 5, and 6 — so the sequence is not an AP. A is false, but R is also false.
Difficulty Level: Moderate
Q3. Assertion (A): The sum of the first $n$ terms of an AP is given by $S_n=\frac{n}{2}[2 a+(n-1) d]$.
Reason (R): This formula is derived by multiplying the nth term with $n$.
Answer: Option (c) is correct.
Explanation: The correct formula is given in A, but the derivation involves pairing terms, not multiplying $a_n \times n$. So R is false.
Difficulty Level: Moderate
Q4. Assertion (A): If the common difference of an AP is zero, then all terms are equal.
Reason $(\mathrm{R})$ : When $d=0$, every term becomes $a+(n-1) \times 0=a$.
Answer: Option (a) is correct.
Explanation: A zero common difference means all terms are equal to the first term aaa. R correctly explains A.
Difficulty Level: Easy
Q5. Assertion (A): The 10th term of an AP is equal to the 5th term.
Reason (R): The common difference of the AP is zero.
Answer: Option (a) is correct.
Explanation: If $a_{10}=a_5$, then
$$
a+9 d=a+4 d \Rightarrow d=0
$$
So all terms are equal. $R$ explains $A$.
Difficulty Level: Moderate
Also check
- Some Applications of Trigonometry Class 10 Assertion Reason Questions Maths Chapter 9
- Introduction to Trigonometry Class 10 Assertion Reason Questions Maths Chapter 8
- Coordinate Geometry Class 10 Assertion Reason Questions Maths Chapter 7
- Triangles Class 10 Assertion Reason Questions Maths Chapter 6
- Arithmetic Progressions Class 10 Assertion Reason Questions Maths Chapter 5
- Quadratic Equations Class 10 Assertion Reason Questions Maths Chapter 4
- Pair of Linear Equations in Two Variables Class 10 Assertion Reason Questions Maths Chapter 3
- Polynomials Class 10 Assertion Reason Questions Maths Chapter 2
- Real Numbers Class 10 Assertion Reason Questions Maths Chapter 1
Topics from which assertion reason questions may be asked
- nth Term of an AP
- Sum of First n Terms
- Applications
Arithmetic progressions are patterns in numbers that show consistent change.
Assertion reason questions from the above given topic may be asked.
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Frequently Asked Questions (FAQs) on Arithmetic Progressions Assertion Reason Questions Class 10
Q1: What does the chapter ‘Arithmetic Progressions’ cover?
A1: It builds key concepts related to arithmetic progressions and prepares you for logical reasoning-based questions.
Q2: What are assertion reason questions?
A2: These consist of two statements: an assertion and a reason. Students need to determine their correctness and relationship.
Q3: Why practice assertion reason questions in Arithmetic Progressions?
A3: They strengthen core concepts and boost confidence in tackling tricky scenarios from arithmetic progressions.
Q4: Are assertion reason questions part of CBSE board exams?
A4: Yes, they are included under competency-based formats to test depth of understanding.
