Find the sum of all natural numbers between $200$ and $400$ which are divisible by $7$.
Step-by-Step Solution
Key Concept: Numbers: $203, 210, \dots, 399$. $a = 203, d = 7, l = 399$. $399 = 203 + (n - 1)7 \Rightarrow (n - 1)7 = 196 \Rightarrow n = 29$. $S_{29} = \dfrac{29}{2}(203 + 399) = 29 \times 301 = 8729$.
$399 = 203 + (n - 1)7 \Rightarrow n = 29$. [1.0 Mark]
$S_{29} = \dfrac{29}{2}(602) = 29 \times 301 = 8729$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Finding $n = 29$: 1.0 Mark
Evaluating sum $= 8729$: 1.0 Mark
Correct Answer: