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Question

(D) The sequence of the first $n$ natural numbers is $1, 2, 3, 4, \dots, n$,which forms an Arithmetic Progression $(A.P.)$ with the first term $a = 1$

Vedclass · Accepted Answer

$\frac{n(n + 1)}{2}$

Vedclass · Answer

(D) The sequence of the first $n$ natural numbers is $1, 2, 3, 4, \dots, n$,which forms an Arithmetic Progression $(A.P.)$ with the first term $a = 1$ and common difference $d = 1$.The formula for the sum of the first $n$ terms of an $A.P.$ is $S_n = \frac{n}{2}[2a + (n - 1)d]$.Substituting the values $a = 1$ and $d = 1$ into the formula:$S_n = \frac{n}{2}[2(1) + (n - 1)(1)]$$S_n = \frac{n}{2}[2 + n - 1]$$S_n = \frac{n(n + 1)}{2}$.

The sum of the first $n$ natural numbers is:

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