Discussion
What will be the sum of the first 20 odd natural numbers ?
Answer: C
The sum is 400.
The sum of the first n odd natural numbers is always \(n^{2}\): 1 = 1, 1 + 3 = 4, 1 + 3 + 5 = 9, and so on. For n = 20:
\[ 1 + 3 + 5 + \dots + 39 = 20^{2} = 400 \]
The same result comes from the arithmetic series formula: 20 terms with average (1 + 39)/2 = 20 give 20 × 20 = 400. 210 is the sum of the first 20 natural numbers, and 420 is the sum of the first 20 even numbers, 2 + 4 + ... + 40.
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