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Question

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


A

625

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B

675

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C

700

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D

650

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Solution

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 an = a + (n−1) d, finding n , we have

49 = 1 + (n−1) x 2

49 = 1 + 2n − 2

50 = 2n

n = 502 = 25

Sum of terms, Sn = n2(a + l)

S25 = 252(1+49) = 252(50) = 25×25 = 625


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