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Question

# Find the sum of all natural numbers between 250 and 1000 which are exactly divisible by 3.

A

156375

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B

156324

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C

147687

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D

156342

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Solution

## The correct option is A 156375 Clearly, the numbers between 250 and 1000 which are divisible by 3 are 252, 255, 258 ....999. This is an A.P. with first term a = 252, common difference = 3 and last term = 999. Let there be n terms in this A.P. Then, an = 999 a + (n – 1) d = 999 252 + (n – 1) × 3 = 999 n = 250 Required sum = Sn = (n2) [a + l] = (2502) [252 + 999] = 156375

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