Question

Find the sum of all 3 digit number which leaves a reminder 5 when divided by 8​

Answer 1

Answer:

62037

Step-by-step explanation:

The sum of all 3 digit numbers which leave 5 as remainder when divided by 8 is 62037

Answer 2

$\red{\large\mathfrak {question}} \:$

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Find the sum of all 3 digit number which leaves a reminder 5 when divided by 8.

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$\green{\large\mathfrak {anwser}}$

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Three digit nos -

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100, 101, 102 _ _ _ _ _ 999

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Three digit nos. which leaves remainder 5 when divided by 8

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101, 109, 117_ _ _ _ _ _997

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$\sf \: {a}_{n} \: = \: a + (n - 1)d$

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997 = 101 + (n - 1)8

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997 - 101 = 8n - 8

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896 = 8n - 8

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$\sf \: n = \dfrac{904}{8}$

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$\sf \implies n = 113$

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$\sf \: \implies {S}_{n} = \dfrac{n}{2} (a + l)$

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$\sf \: \implies {S}_{113} = \dfrac{113}{2} (101 + 997)$

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$\sf \implies {S}_{113} = \dfrac{113}{2} (1098)$

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$\sf \: \implies{S}_{113} = 113 \times 549$

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$\sf \implies {S}_{113} = 62037$

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$\pink{\large\mathfrak {!! \: hope \: it \: helps \: you \: !!}}</p><p>$