Question

The sum of all odd numbers lying between 20 and 50 is equal to

• A. 425
• B. 525
• C. 625
• D. 725

Answer 1

The correct option is B 525

Odd numbers between 20 and 50 are 21, 23, 25, … 49.
They form an AP with first term (a) = 21 and common difference (d) = 2.
$a_n=a+(n–1)d$
$\Rightarrow 49=21+(n–1)2$
$\Rightarrow \frac{49-21}{2}=n-1$
$\Rightarrow 14+1=n$
$\Rightarrow n=15$
Thus, there are 15 odd numbers in between 20 and 50
Now, $S_{15}=\frac{15}{2}\{2\times 21+(15-1)\times 2\}$ (As $S_n=\frac{n}{2}\{2a+(n-1\left)d\right\}$)
$\Rightarrow S_{15}=15(21+14)$
$\Rightarrow S_{15}=15\times 35$
$\Rightarrow S_{15}=525$
Therefore, the sum of all odd numbers lying between 20 and 50 is 525.
Hence, the correct answer is option (2).