Question

Find the sum of all the odd positive integers less than $100$.

• A. $2400$
• B. $2500$
• C. $2525$
• D. $2600$
• E. $2650$

Answer 1

The correct option is B $2500$

The possible odd positive integers: $1,3,5,7,9,\mathrm{11..........99}$
The first term, $a$ $=1$
The difference between two consecutive terms $=3-1=2$
The total no. of terms $=50$
Applying sum of arithmetic progression formula,
$S_n=\frac{n}{2}[2a+(n-1\left)d\right]$
$=\frac{50}{2}[2\times 1+(50-1\left)2\right]$
$=25(2+98)=2500$
Hence, choice B is correct.