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Question
Find the sum of all three-digits natural numbers which are divisible by 13.
Solution
All three-digit numbers which are divisible by 13 are 104, 117, 130, 143,.…… 938.
This is an AP in which a = 104, d = (117 – 104) = 13 and l = 938
Let the number of terms be n
Then Tn = 938
⇒ a + (n-1) d = 988
⇒ 104+(n-1) × 13 = 988
⇒13n = 897
⇒ n = 69
∴ Required sum = `n/2 (a+l)`
`= 69/2 [ 104+988] = 69 × 546 = 37674`
Hence, the required sum is 37674.
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