Assertion (A): Common difference of the AP : 5, 1, -3, -7, … is 4. Reason (R): Common difference of the AP : a_1, a_2, a_3, …, a_n is obtained by d = a_n - an-1. Select the correct answer from the codes (A), (B), (C) and (D) given below. (A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A). (B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A). (C) Assertion (A) is true, but Reason (R) is false. (D) Assertion (A) is false, but Reason (R) is true.

MathsCBSE Class 10 · Standard · Board exam 2025, set 30/2/1 · 1 mark · Assertion-reason

CBSE Class 10 Mathematics Standard 2025: question 19

Set in the CBSE Class 10 board exam of 2025, paper 30/2/1, section A, question 19, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q19 · 1 mark · Assertion-reasonCompetency-basedArithmetic Progressions

Assertion (A): Common difference of the AP : $5, 1, - 3, - 7, \dots$ is $4$ .

Reason (R): Common difference of the AP : $a_{1}, a_{2}, a_{3}, \dots, a_{n}$ is obtained by $d = a_{n} - a_{n - 1}$ .

Select the correct answer from the codes (A), (B), (C) and (D) given below.

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

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/2/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

Common difference is a term minus the term before it.

Hint 2

Compute $1 - 5$ carefully, watching the sign.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

Assertion: $d = 1 - 5 = - 4$ , not $4$ , so (A) is false.
½ mark
Reason: in an AP, $d = a_{n} - a_{n - 1}$ (any term minus its preceding term), so (R) is true. Hence option (D).
½ mark

Answer: Option (D)

Where the marks are

Finds $d = - 4$ , so Assertion false; Reason true; chooses (D) (1 mark)

Revise the chapter

Chapter: Arithmetic Progressions (notes, formulas, where marks are lost and every past question)

Practise this chapterBoard-style questions from Arithmetic Progressions, one at a time, marked against the answer key and marking points.Back to the full paper2025 board paper, set 30/2/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2025: question 19

Hints

Step-by-step solution

Revise the chapter

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