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Question
Write the sum of first n even natural numbers.
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Solution
We need to find the sum of 2, 4, 6, 8...upto n terms.
Here, a = 2, d = 2
We know:
\[S_n = \frac{n}{2}\left\{ 2a + \left( n - 1 \right)d \right\}\]
\[ = \frac{n}{2}\left\{ 2 \times 2 + \left( n - 1 \right)2 \right\}\]
\[ = n\left( n + 1 \right)\]
Therefore, the sum of the first n odd numbers is \[n\left( n + 1 \right)\] .
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