Assertion and Reason Questions for Class 10 Maths Chapter 5 Arithmetic Progression PDF

Assertion And Reason Questions for Class 10 Maths Chapter 5 Arithmetic Progressions are available in this Maths article. Assertion And Reason Questions for Class 10 Maths Chapter 5 Arithmetic Progressions are very useful to solve the problems easily. This article helps the students to know the key questions and answers about Arithmetic Progressions. Arithmetic progressions help us understand patterns where numbers increase or decrease by a fixed difference, which we use in everyday calculations. Our subject experts have provided detailed solutions for these problems based on the CBSE syllabus and the NCERT textbook. This material helps students revise the chapter easily and perform well in the final examination. A free downloadable PDF is also available for easy practice and revision.

Important Assertion And Reason Questions on Arithmetic Progression 

Directions: In the following questions a statement of assertion (A) is followed by a statement of reason(R). Mark the correct choice as:

Choose the correct option for the following questions:

• (A). Both Assertion (A) and Reason (R) are true, and Reason is the correct explanation of Assertion.

• (B). Both Assertion (A) and Reason (R) are true, but Reason is not the correct explanation of Assertion.

• (C). Assertion (A) is true, but Reason (R) is false.

• (D). Assertion (A) is false, but Reason (R) is true.

Question 1:

Assertion (A): A sequence in which the difference between consecutive terms remains constant is called an Arithmetic Progression (AP).

Reason (R): The constant difference in an AP is called the common difference.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 2:

Assertion (A): The sequence 2,5,8,11,142, 5, 8, 11, 142,5,8,11,14 is an AP.

Reason (R): The difference between consecutive terms is 3.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 3:

Assertion (A): The nth term of an AP is given by:

dan=a+(n−1)d

Reason (R): Here, aaa is the first term and ddd is the common difference.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 4:

Assertion (A): The sequence 7,7,7,77, 7, 7, 77,7,7,7 is an AP.

Reason (R): The common difference of the sequence is 0.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 5:

Assertion (A): The 10th term of the AP 3,6,9,12,... is 30.

Reason (R): For this AP,a=3 and d=3

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

a10=3+(10−1)×3=30

Question 6:

Assertion (A): The sum of the first nnn terms of an AP is given by:

Sn=n2[2a+(n−1)d]

Reason (R): The formula depends on the first term, common difference, and number of terms.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 7:

Assertion (A): The sequence 1,4,9,16,25 is an AP.

Reason (R): The difference between consecutive terms is not constant.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (D). A is false, but R is true.

Question 8:

Assertion (A): If the common difference of an AP is positive, the sequence increases.

Reason (R): Each term becomes greater than the previous term.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 9:

Assertion (A): The common difference of the AP 15,10,5,0,−515, 10, 5, 0, -515,10,5,0,−5 is -5.

Reason (R): The common difference is found by subtracting a term from the next term.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 10:

Assertion (A): The AP 5,8,11,14,...5, 8, 11, 14, ...5,8,11,14,... has common difference 3.

Reason (R): The difference between any two consecutive terms is constant.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 11:

Assertion (A): The nth term of an AP depends on the common difference.

Reason (R): Changing the common difference changes the sequence.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 12:

Assertion (A): The sum of the first 5 natural numbers is 15.

Reason (R): Natural numbers form an AP with first term 1 and common difference 1.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

1+2+3+4+5=15

Question 13:

Assertion (A): An AP can have negative terms.

Reason (R): The common difference of an AP can be negative.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 14:

Assertion (A): The sequence 20,17,14,11,820, 17, 14, 11, 820,17,14,11,8 is a decreasing AP.

Reason (R): Its common difference is negative.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 15:

Assertion (A): The formula for the nth term helps find any term without writing the whole AP.

Reason (R): The nth term formula directly gives the required term number.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

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