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Que 2. Sum of 3 digit numbers divided by 5 gives the remainder of 3 ?
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Answer:
Smallest 3 digit natural number divisible by 3=102
Largest 3 digit natural number divisible by 3=999
∴3 digit number divisible by 3 are:
102,105,108,.....999
this is an AP with a=102 and d=3
no.of terms
999=a+(n−1)d
999=102+(n−1)3
3
897
=(n−−)⇒(n−1)=299
∴n=300
Sum of all numbers = Sum of 300 terms of AP
=
2
300
[2a+)300−1)d]
=
2
300
[2×(102)+(299)3]
=(150)[204+891]
Sum of all number of series =(150)[1101]=165150
∴ Sum of all 3 digit number divisible by 3 is 165150
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