Q1. [1] § 5.2 Arithmetic Progressions § 5.5 Summary
Directions: A statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option. Assertion (A): For an A.P., 3,6,9, …, 198, 10th term from the end is 168. Reason (R): If 'a' and '$l$' are the first term and last term of an A.P. with common difference 'd', then nth term from the end of the given A.P. is $l - (n - 1) d$.
- 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 (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 30/5/1 Q20
Generated by claude-sonnet-4-6 · 2026-06-15 10:33 · grounding rag
Model Answer
Option (A)
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
Verification: For AP 3, 6, 9, …, 198: $l = 198$, $d = 3$, so 10th term from end $= 198 - (10-1) \times 3 = 198 - 27 = 171$.
Wait — the calculated value is 171, not 168, so Assertion (A) is false.
Correct Option: D — Assertion (A) is false, but Reason (R) is true.
Explanation
- The formula in R is correct: nth term from end $= l - (n-1)d$.
- Applying it: $198 - 9 \times 3 = 198 - 27 = 171 \neq 168$, so A is false.
- Always verify the assertion numerically before choosing option A; do not assume both are true just because the formula looks right.
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