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Find the sum of 2,4,6,8,,,........2n

Question

Find the sum of $2, 4, 6, 8,,, ........2 n$

n (n + 1)

n^{2}

n (n - 1)

n^{2} + n

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Find the sum of

2, 4, 6, 8,,, ........2 n

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Text solutionVerified

The given sequence is

2, 4, 6, 8, .....2 n

∴ a = 2, d = 2

a_{k} = 2 n

∴ 2 n = a + (k - 1) d

\Rightarrow 2 n = 2 + (k - 1) 2

\Rightarrow k = n

Sum of

n

terms

= \frac{k}{2} (2 a + (k - 1) d)

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

= n (n + 1)

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