Arithmetic Progressions
NCERT Exemplar Ch 05
CBSE_NCERT_EXEMPLAR_CH05
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:
$26$
$27$
$28$
$29$
Step-by-Step Solution
Key Concept: $a_n = S_n - S_{n-1}$.
Stepwise Solution:
$a_n = (3n^2 + 5n) - [3(n-1)^2 + 5(n-1)] = 6n + 2$. [0.5 Mark]
Set $a_m = 6m + 2 = 164 \Rightarrow 6m = 162 \Rightarrow m = 27$. [0.5 Mark]
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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