Question

Find the sum of the odd numbers between 0 and 50 .
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Answer 1

Answer:

Answer. =625. Therefore the sum of all odd numbers between 0 and 50 is 625.Mar 17, 2016

Answer 2

$\bf{\underline{Solution}}:-$

➟ Sum of all odd numbers between 0 and 50 are 1,3,5,7,9,.............,49.

Given :-

• First term (a) = 1

• Common difference (d) = 3 - 1 = 2

• nth term (an) = 49

To find :-

• The sum of the odd numbers between 0 and 50

Solution :-

At first we need to find an,

we know that,

$\blue{\bigstar}\:\:{\underline{\boxed{\bf\red{a_n=a+(n-1)d}}}}$

$\rm\longrightarrow\:49=1+(n-1)\times{2}$

$\rm\longrightarrow\:49-1=(n-1)\times{2}$

$\rm\longrightarrow\:48=(n-1)\times{2}$

$\rm\longrightarrow\:\cancel\dfrac{48}{2}=n-1$

$\rm\longrightarrow\:24=n-1$

$\rm\longrightarrow\:24+1=n$

$\rm\longrightarrow\:25=n$

$\rm\longrightarrow\:n=25$

Now,

By using formula of Sn,

$\orange{\bigstar}\:\:{\underline{\boxed{\bf\pink{s_n=\dfrac{n}{2}\:[2a+(n-1)d]}}}}$

$\rm\longrightarrow\:s_n=\dfrac{25}{2}\:[2\times{1}+(25-1)\times{2}]$

$\rm\longrightarrow\:s_n=\dfrac{25}{2}\:[2+24\times{2}]$

$\rm\longrightarrow\:s_n=\dfrac{25}{2}\:[2+48]$

$\rm\longrightarrow\:s_n=\dfrac{25}{2}\times{50}$

$\rm\longrightarrow\:s_n=25\times{25}$

$\rm\longrightarrow\:s_n=625$

Hence,the sum of the odd numbers between 0 and 50 will be 625.