Q1. [1]
Assertion (A) : Common difference of the AP : $5, 1, -3, \ldots$ is $4$.
Reason (R) : Common difference of the AP : $a_1, a_2, a_3, \ldots$ 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.
Previously asked in CBSE board exam
2025 30/2/1 Q19
Generated by claude-sonnet-4-6 · 2026-06-15 10:30 · grounding rag
Model Answer
(D) Assertion (A) is false, but Reason (R) is true.
The common difference of AP: 5, 1, −3, … is $d = 1 − 5 = −4$, not 4. The Reason is correct as $d = a_n − a_{n−1}$.
Source: Chapter 5, Section 5.1 / Summary Point 2
Explanation
- The Assertion gives $d = 4$, which is wrong; the correct value is $d = -4$ (each term decreases by 4).
- The Reason correctly states the formula for common difference, so R is true.
- Since A is false but R is true, option (D) is correct.
- Always verify the sign when calculating common difference — a common mistake is ignoring the negative sign.
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