Question

Find the sum of all natural numbers between 20 and 40​

Answer 1

★ Answer ★

Let's understand the concept first .

★ Natural Numbers ★

• All such counting numbers are referred as natural numbers. It is denoted by " N ".

Examples :- { 1 , 2 , 3 , 4 , ········ }

Thus,

Sum of all natural numbers between 20 and 40.

➹ Numbers between 20 and 40 are :-

21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39 → 19 Natural numbers$.$

Hence, we are going to use the formula of sum of an A. P

Here, we got

➹ a ( First term) → 21

➹ d ( Common difference) → 1

➹ n ( No. of terms) → 19

Formula Required :-

Sum of nth term of an A.P. is denoted by the formula:-

$\sf{S_n = \dfrac{n}{2}[2a + (n-1)d]}$

Where the values of a, d and n are same.

We have the values a, n and d which we are going to put in the formula in order to get the value of $\sf{S_n}$

_____________________

a = 5

d = 3

$\sf{a_n = 19}$

To find:-

n and $\sf{S_n}$

Solution:-

We know,

In an A.P.

$\sf{S_n = \dfrac{n}{2}[2a + (n-1)d]}$

= $\sf{S_{19} = \dfrac{19}{2}[2\times21 + (19-1)\times 1]}$

= $\sf{S_{19} = \dfrac{19}{2}[42+18\times1]}$

= $\sf{S_{19} = \dfrac{19}{2}[60]}$

= $\sf{S_{19} = 19\times30}$

= $\sf{S_{19} = 570}$

Therefore,

$\sf{S_n = 570}$

_____________________

Note :-You can see the answer in the attachment also, if not visible in app.

Answer 2

$\huge\sf\underline{Solution}$

Step by step explanation:-

First We will see What are the natural numbers between 20 and 40

21, 22, 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 ,35, 36 ,37 , 38 , 39

So, We got a sequence First we will check It is In AP, HP or GP

First we will check their difference

22 - 21 = 1

23 - 22 = 1

24 - 23 = 1

Their difference is same Hence It is in AP

So,

In AP

First term is denoted by = a

Commondifference is = d

Number of terms is denoted by = n

So,

In given sequence

a = 21

d = 1

n = 19

Sum of terms is denoted by Sn

Sn = $\frac{n}{2}$ (2a + (n-1) d

Sn = $\frac{19}{2}$ [2×21 + (19-1) 1]

Sn = $\frac{19}{2}$ [2×21 +18]

Sn = $\frac{19}{2}$ ×42+18

Sn = $\frac{19}{2}$ ×60

Sn = 19 × 30

Sn = 570

So, The sum of all natural numbers between 20 and 40 is 570

U can do In another method that is

Write all numbers between 20 and 40 Do addition ...

before method is easy to find their sum Instead of doing addition