Question

How to find the sum of odd numbers from 1 to 9 without adding them?

Answer 1

Given odd number from 1 to 9.

1+3+5+7+9

Ok dont need to add them

This is an AP with:

a=1

d=3-1=2

n=5

Sn=n/2*[2a+(n-1)d]

Sn=5/2*[2+4*2]

Sn=5/2*10

=5*5

=25

This is a labourous process:

Adding is easier

Hope it helps you.

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Answer 2

$\mathfrak{\huge{\underline{\blue{Formula}}}}$

¶¶¶
$Sum\: of first 'n'\: Odd\: Numbers = n^{2}$

¶¶¶
In first 'm' Natural No.s ,

• $there\: are\: \frac{m}{2} Odd\: No.s ; if\: m-even$

• $there\: are\: \frac{m+1}{2} Odd\: No.s ; if m-odd$

^^ Both the No.s(1 & m) are Included

$\mathbb{\underline{\blue{SOLUTION:}}}$

Now,
From 1 - 9, [m = 9(odd)]

$No. of Odd No.s 'n'= \frac{9+1}{2}$

$= \frac{10}{2}$

•°• n= 5

•°• $\underline{\underline{Required\: Sum = 5^{2} = 25}}$

$\mathfrak{\huge{\pink{Cheers}}}$

$\mathcal{\huge{\orange{Hope\: it\: Helps}}}$