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Question

Find the sum of all natural numbers between 100 and 500 which are divisible by 7.

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Solution

All the natural numbers less than 100 and divisible by 6 are 6, 12, 18, 24,...,96.
This is an AP in which a = 6, d = (12 - 6) = 6 and l = 96.
Let the number of terms be n.
Then Tn = 96
⇒ a + (n - 1)d = 96
⇒ 6 + (n - 1​) ⨯​ 6 = 96
⇒ 6n = 96
⇒ n = 16

∴ Required sum = n2a+l
= 1626 + 96 = 8×102 = 816
Hence, the required sum is 816.

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