Question

Find the sum of odd numbers between $0$ and $90$.

• A. $2025$
• B. $2020$
• C. $2035$
• D. $2041$

Answer 1

The correct option is A $2025$

The sum of first n terms of arithmetic series formula can be written as,
$S_n=\frac{n}{2}[2a+(n-1\left)d\right]$ ............ (1)
The list of odd numbers between $0$ and $90$ is $1,3,5,7,9,..........89$
Where $n=$ number of terms
$a=$ first odd number $\Rightarrow$ $1$
$d=$ common difference of A.P. $\Rightarrow 2$
$T_n=$ Last term $\Rightarrow$ 89
$T_n=a+(n-1)d$
$89=1+(n-1)2$
$89=1+2n-2$
$89-1+2=2n$
$90=2n$
$n=45$
Apply the given data in the formula (1),
$S_{45}=\frac{45}{2}[2\times 1+(45-1\left)2\right]$
$=22.5[2+(44\left)2\right]$
$=22.5[2+88]$
$=22.5\left[90\right]$
$=2025$
So, the sum of odd numbers between $0$ and $90$ is $2,025$.