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Arithmetic Progressions
CBSE 2026 Board Exam Set 3 (Code 30/1/3)
CBSE_BOARD_PYQ_2026_30_1_3
Grade 10

Question:

[Section A]

Assertion (A): The $n^{\text{th}}$ term of an AP whose sum of first $n$ terms is $S_n = 3n^2 + 2n$ is $6n - 1$.
Reason (R): The $n^{\text{th}}$ term of an AP is given by $a_n = S_n - S_{n-1}$.

Step-by-Step Solution

Key Concept: $a_n = S_n - S_{n-1} = (3n^2+2n) - (3(n-1)^2+2(n-1)) = 6n-1$.
$a_n = (3n^2+2n) - (3n^2 - 6n + 3 + 2n - 2) = 6n - 1$. Both A and R are true. [1.0 Mark]

Correct Answer: (b) Both Assertion (A) and Reason (R) are true, but Reason (R) is NOT the correct explanation of Assertion (A).
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