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Arithmetic Progressions

CH05 Question Bank

CBSE_CH05_QUESTION_BANK

Grade 10

Question:

If the sum of the first $n$ terms of an AP is $S_n = 3n^2 + 5n$, the common difference is:

$3$
$5$
$6$
$8$

Step-by-Step Solution

Key Concept: Find $a_1$ and $a_2$ using $S_1$ and $S_2-S_1$, then subtract.

$a_1=S_1=8$. $S_2=3(4)+5(2)=22$, so $a_2=S_2-S_1=22-8=14$. [0.5 Mark]

$d=a_2-a_1=14-8=6$. [0.5 Mark]

Correct Answer: $6$

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