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Arithmetic Progressions
CH05 Question Bank
CBSE_CH05_QUESTION_BANK
Grade 10

Question:

Find the sum of all natural numbers between $100$ and $200$ which are divisible by $9$.

Step-by-Step Solution

Key Concept: Identify the relevant AP first, then apply the sum formula.
The multiples of $9$ between $100$ and $200$ are $108,117,\ldots,198$, with $a=108,d=9,l=198$. Number of terms: $198=108+(n-1)9\Rightarrow n=11$. [1.0 Mark]

$S_{11}=\dfrac{11}{2}(108+198)=\dfrac{11}{2}(306)=11\times153=1683$. [1.0 Mark]

Correct Answer:
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