Question:
What is the sum of all natural numbers strictly between 100 and 1000 which are multiples of 5?
What is the sum of all natural numbers strictly between 100 and 1000 which are multiples of 5?
Show Hint
For AP sums, always prefer:
\[
S=\frac{n}{2}(a+l)
\]
when first and last terms are easily identifiable.
Updated On: Jun 12, 2026
- \(97,450\)
- \(98,450\)
- \(98,550\)
- \(97,650\)
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Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Identify the AP. Multiples of 5 between 100 and 1000: First term: \[ 105 \] Last term: \[ 995 \] Common difference: \[ d=5 \]
Step 2: Find number of terms. \[ n=\frac{995-105}{5}+1 \] \[ =\frac{890}{5}+1 \] \[ =178+1=179 \]
Step 3: Use sum formula. \[ S_n=\frac{n}{2}(a+l) \] \[ S=\frac{179}{2}(105+995) \] \[ =\frac{179}{2}(1100) \] \[ =179\times 550 \] \[ =98450 \] \[ \boxed{98,450} \]
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