Q :  14        Find the sum of the odd numbers between \small 0 and \small 50.

Answers (1)

Odd number between 0 and 50 are  
1,3,5,...49
This is an AP with 
here, \ a = 1 \ and \ d = 2
There are total 25 odd number between 0 and 50
Now, we know that 
S_n= \frac{n}{2}\left \{ 2a+(n-1)d \right \}
\Rightarrow S_{25}= \frac{25}{2}\left \{ 2\times 1+(25-1)2 \right \}
\Rightarrow S_{25}= \frac{25}{2}\left \{ 2+48 \right \}
\Rightarrow S_{25}= \frac{25}{2}\times 50
\Rightarrow S_{25}= 25 \times 25 = 625
Therefore,  sum of the odd numbers between \small 0 and \small 50  625

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