Arithmetic Progressions
CBSE 2026 Board Exam Set 3 (Code 30/1/3)
CBSE_BOARD_PYQ_2026_30_1_3
Grade 10
Question:
[Section C]
The sum of the first $n$ terms of an AP is given by $S_n = 3n^2 + 5n$. Find the $15^{\text{th}}$ term of this AP.
Step-by-Step Solution
Key Concept: $a_n = S_n - S_{n-1} \Rightarrow a_{15} = S_{15} - S_{14}$.
$S_{15} = 3(225) + 5(15) = 675 + 75 = 750$. $S_{14} = 3(196) + 5(14) = 588 + 70 = 658$. $a_{15} = 750 - 658 = 92$. (Alternatively, $a_n = 6n + 2 \Rightarrow a_{15} = 92$). [3.0 Marks]
Correct Answer: 92
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