Question

Find the sum of all odd natural numbers from 20 to 60

Answer 1

Answer:800

Step-by-step explanation:21+23+25+.......+59=

n/2 ×(a+l)=20/2 (21+59)=10×80=800

Answer 2

Given,

All odd natural numbers from 20 to 60.

To find,

Sum of these numbers.

Solution,

Firstly, we need to know all the odd natural numbers between 20 and 60. So, these numbers are,

21, 23, 25, 27,....., 59.

We can see that this is an A. P. and last number in this A. P. will be 59, as it is only odd natural number before 60.

Now, we can solve this problem by using the relation for sum of all terms in an A. P. That is,

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

Where,

n = number of terms in A. P.

a = first term,

d = common difference.

Before calculating the sum, we need to know n, that is number of terms. This can be found using the formula for any $n^{th}$ term as,

$a_n=a+(n-1)d$

Substituting $a_n=59,a = 21,d=2$

⇒ $59=21+(n-1)2$

Rearranging and simplifying,

$2(n-1)=38$

⇒ $n-1=19$

⇒ $n=20$

So, we have 20 odd natural numbers from 20 to 60.

Now, substituting $a_n, n, a,d$ in the formula for $S_n$

⇒ $S_n=\frac{20}{2} [2(21)+(20-1)2]$

⇒ $S_n=10 [42+38]$

⇒ $S_n= 800$

Therefore, the sum of all odd natural numbers from 20 to 60 will be 800.