Sum of first n natural numbers is

English

Gujarati

Hindi

8. Sequences and Series

normal

The sum of first $n$ natural numbers is

A

$n\,(n - 1)$

B

$\frac{{n\,(n - 1)}}{2}$

C

$n\,(n + 1)$

D

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

Solution

(d) We know that natural numbers are $1,\;2,\;3,\;4,\;……..n$ are in $A.P.$

Now sum $ = \frac{n}{2}[2 \times 1 + (n – 1)1] = \frac{n}{2}(n + 1)$.

Standard 11

Mathematics

Share

Similar Questions

If $n$ arithmetic means are inserted between a and $100$ such that the ratio of the first mean to the last mean is $1: 7$ and $a+n=33$, then the value of $n$ is

hard

(JEE MAIN-2022)

If the first term of an $A.P.$ is $3$ and the sum of its first four terms is equal to one-fifth of the sum of the next four terms, then the sum of the first $20$ terms is equal to

hard

(JEE MAIN-2025)

Find the sum of all numbers between $200$ and $400$ which are divisible by $7.$

medium

Let $a_{1}, a_{2}, \ldots \ldots, a_{21}$ be an $A.P.$ such that $\sum_{n=1}^{20} \frac{1}{a_{n} a_{n+1}}=\frac{4}{9}$. If the sum of this AP is $189,$ then $a_{6} \mathrm{a}_{16}$ is equal to :

hard

(JEE MAIN-2021)

Let $a_1, a_2, a_3 \ldots$ be in an $A.P.$ such that $\sum_{ k =1}^{12} a _{2 k -1}=-\frac{72}{5} a _1, a _1 \neq 0$. If $\sum_{ k =1}^{ n } a _{ k }=0$, then $n$ is:

medium

(JEE MAIN-2025)