Question

Find the sum of all odd numbers between 0 and 50.

• A. 625
• B. 675
• C. 700
• D. 650

Answer 1

The correct option is A

625

The odd numbers between 0 and 50 are 1, 3, 5, 7, ..., 49.

It is an arithmetic progression because the difference between consecutive terms is constant (equal to 2).

First term = a = 1

Common difference = 3 - 1 = 2

Last term = l = 49

We do not know how many odd numbers are present between 0 and 50. Therefore, we need to find n first.

Using formula $a_n$ = a + (n−1) d, finding n , we have

49 = 1 + (n−1) x 2

$\Rightarrow$ 49 = 1 + 2n − 2

$\Rightarrow$ 50 = 2n

$\Rightarrow$ n = $\frac{50}{2}$ = 25

Sum of terms, $S_n$ = $\frac{n}{2}$(a + l)

$S_{25}$ = $\frac{25}{2}(1+49)$ = $\frac{25}{2}$(50) = $25\times 25$ = 625