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Arithmetic Progressions
CH05 Question Bank
CBSE_CH05_QUESTION_BANK
Grade 10

Question:

Find the sum of all natural numbers less than $100$ which are NOT divisible by $4$.

Step-by-Step Solution

Key Concept: Find the sum of all natural numbers 1 to 99, then subtract the sum of the multiples of 4 in that range.
Sum of natural numbers $1$ to $99$: $S=\dfrac{99\times100}{2}=4950$. [1.0 Mark]

Multiples of $4$ below $100$: $4,8,\ldots,96$; $n=24$ terms; sum $=\dfrac{24}{2}(4+96)=12\times100=1200$. [1.0 Mark]

Required sum $=4950-1200=3750$. [1.0 Mark]

Correct Answer:
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