Find the sum of all multi-digit natural numbers less than $1000$ which are divisible by $5$.
Step-by-Step Solution
Key Concept: Multiples: $10, 15, 20, \dots, 995$. $a = 10, d = 5, l = 995$. $995 = 10 + (n - 1)5 \Rightarrow (n - 1)5 = 985 \Rightarrow n = 198$. $S_{198} = \dfrac{198}{2}(10 + 995) = 99 \times 1005 = 99495$.
$10 + (n - 1)5 = 995 \Rightarrow n = 198$. [1.0 Mark]
$S_{198} = 99 \times (10 + 995) = 99 \times 1005 = 99495$. [2.0 Marks]
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🎯 Official CBSE Marking Scheme:
Finding $n = 198$: 1.0 Mark
Evaluating sum $= 99495$: 2.0 Marks
Correct Answer: