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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