Find the sum of all three-digit natural numbers which are multiples of $7$.
Step-by-Step Solution
Key Concept: First: $105$, Last: $994$. $994 = 105 + (n - 1)7 \Rightarrow (n - 1)7 = 889 \Rightarrow n = 128$. $S_{128} = \dfrac{128}{2}(105 + 994) = 64 \times 1099 = 70336$.
$105 + (n - 1)7 = 994 \Rightarrow n = 128$. [1.0 Mark]
$S_{128} = 64 \times (105 + 994) = 64 \times 1099 = 70336$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Finding $n = 128$: 1.0 Mark
Evaluating sum $= 70336$: 1.0 Mark
Correct Answer: