The sum of the first n even natural numbers i | vedclass

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(C) The first $n$ even natural numbers are $2, 4, 6, \dots, 2n$.This forms an Arithmetic Progression $(AP)$ where the first term $a = 2$ and the commo

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$n(n+1)$

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(C) The first $n$ even natural numbers are $2, 4, 6, \dots, 2n$.This forms an Arithmetic Progression $(AP)$ where the first term $a = 2$ and the common difference $d = 2$.The sum of the first $n$ terms of an $AP$ is given by the formula $S_n = \frac{n}{2}[2a + (n - 1)d]$.Substituting the values: $S_n = \frac{n}{2}[2(2) + (n - 1)2]$.$S_n = \frac{n}{2}[4 + 2n - 2]$.$S_n = \frac{n}{2}[2n + 2]$.$S_n = \frac{n}{2} \cdot 2(n + 1)$.$S_n = n(n + 1)$.

The sum of the first $n$ even natural numbers is............

Similar Questions

Let $S_n$,$S_{2n}$,and $S_{3n}$ be the sums of $n$,$2n$,and $3n$ terms of an Arithmetic Progression $(AP)$,respectively. Prove that $S_{3n} = 3(S_{2n} - S_n)$.

In an $AP$,given $l = 28$,$S = 144$,and there are a total of $9$ terms. Find $a$.

The sum of how many terms of the $A.P.$ $31, 36, 41, \ldots$ is $535$?

Find the sum:
$1+(-2)+(-5)+(-8)+\ldots+(-236)$

Find the sum of the first $25$ terms of the $A.P.$ $3, \frac{9}{2}, 6, \frac{15}{2}, \ldots$

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