Find the sum of all multiples of $9$ lying between $300$ and $700$.
Step-by-Step Solution
Key Concept: Multiples: $306, 315, \dots, 693$. $a = 306, d = 9, l = 693$. $693 = 306 + (n-1)9 \Rightarrow 9n = 396 \Rightarrow n = 44$. $S_{44} = \dfrac{44}{2}(306 + 693) = 22 \times 999 = 21978$.
$306 + (n - 1)9 = 693 \Rightarrow n = 44$. [1.0 Mark]
$S_{44} = 22 \times (306 + 693) = 22 \times 999 = 21978$. [2.0 Marks]
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🎯 Official CBSE Marking Scheme:
Finding $n = 44$: 1.0 Mark
Evaluating sum $= 21978$: 2.0 Marks
Correct Answer: