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What is the sum of the first n even natural numbers?
1. 2n
2. n2
3. n2 - 1
4. n2 + n

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Correct Answer - Option 4 : n2 + n

Concept:

Sum of n terms of AP = \(\rm \frac{n}{2} [2a + (n - 1)d]\)

Where, a = first term, d = common difference and n = number of terms

Calculation:

First n even natural numbers: 2, 4, 6, 8,.... 2n

Sum = \(\rm S_{n} = \frac{n}{2} [2a + (n - 1)d]\)

Here, a = 2, d = 4 - 2 = 2

\(\rm S_{n} = \frac{n}{2} [2(2) + (n - 1)2]\)

= n(n + 1)

= n2 + n

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