Question

The average of all odd numbers up to 100 is

• A. $49$
• B. $49.5$
• C. $50$
• D. $51$

Answer 1

The correct option is C $50$

The odd numbers upto 100 are $1,3,5,...99$

There are $50$ odd terms.

sum of the elements is $1+3+5+...+99$

The above terms are in Arithmetic Progression with first term $a=1$ and common difference $d=3-1=2$

sum of $50$ terms is $=\left(\frac{n}{2}\right)[2a+(n-1\left)d\right]$

$=\left(\frac{50}{2}\right)\left[2\right(1)+(50-1\left)2\right]=\left(25\right)(2+98)=25\left(100\right)=2500$

Therefore, $mean=\frac{2500}{50}=50$