Question

The sum of all $2$-digit odd number is

• A. $2475$
• B. $2530$
• C. $4905$
• D. $5049$

Answer 1

The correct option is A $2475$

We have to find the sum $11+13+15+...+99.$

Clearly, the terms of this series form an AP with

first term $a=11$,

common difference $d=2$ and

last term $l=a_n=99$

$\Rightarrow a+(n-1)d=99\Rightarrow 11+(n-1)2=99\Rightarrow n=45$

$\therefore$ Required sum$=S_n=\frac{n}{2}[a+l]$

$=\frac{45}{2}[11+99]=45\times 55=2475$

Therefore, option A is correct.