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Question
Find the sum of first n odd natural numbers.
Solution
The first n odd natural numbers are:
1, 3, 5, 7, 9...
a = 1, d = 2, Total terms = n
\[S_n = \frac{n}{2}\left[ 2a + (n - 1)d \right]\]
\[ \Rightarrow S_n = \frac{n}{2}\left[ 2 \times 1 + (n - 1)2 \right]\]
\[ \Rightarrow S_n = \frac{n}{2}\left[ 2 + (n - 1)2 \right]\]
\[ \Rightarrow S_n = \frac{n}{2}\left[ 2n \right]\]
\[ \Rightarrow S_n = n^2\]
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