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Find the sum of all three digit natural numbers which are divi

Question

Find the sum of all three digit natural numbers which are divisible by 7.

70336

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Text solutionVerified

First no is

105

and last no is

994

t_{n} = a + (n - 1) d

$a =$ First term

$d =$ Common difference

$n =$ number of terms

$t_{n} = n^{t h}$ term

994 = 105 + (n - 1) 7

994 = 105 + 7 n - 7

994 + 7 - 105 = 7 n

896 = 7 n

∴ n = 128

Now, as we know

S_{n} = \frac{n}{2} [2 a + (n - 1) d]

∴

S_{128} = \frac{128}{2} [210 + 889]

......putting

(n = 128)

= 64 \times 1099 = 70336

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Question Text	Find the sum of all three digit natural numbers which are divisible by 7.
Answer Type	Text solution:1
Upvotes	150