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Arithmetic Progressions
NCERT Exemplar
CBSE
Grade 10

Question:

If the sum of the first $n$ terms of an AP is $S_n = 3n^2 + 5n$, then its $m^{\text{th}}$ term is $164$. The value of $m$ is:
(a) $26$
(b) $27$
(c) $28$
(d) $29$

Step-by-Step Solution

Key Concept: $a_n = S_n - S_{n-1}$.
$a_n = (3n^2 + 5n) - [3(n-1)^2 + 5(n-1)] = 6n + 2$. [0.5 Mark]
Set $a_m = 6m + 2 = 164 \Rightarrow 6m = 162 \Rightarrow m = 27$. [0.5 Mark]

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🎯 Official CBSE Marking Scheme:
Finding general term $a_n = 6n + 2$: 0.5 Mark
Solving $6m + 2 = 164 \Rightarrow m = 27$: 0.5 Mark

Correct Answer: $27$
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