Question

If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.

Find the sum of all the multiples of 3 or 5 below 1000.

Answer 1

http://answers.yahoo.com/question/index?qid=20100213122319AAHxFJg

Try this link

Answer 2

consider 3+6+9+......+999 multiples of 3 <1000
here a=3, d=3, l=999
l=a+(n-1)d,find n
\[thenS3=\frac{ n \left( a+l \right) }{ 2 }\]
similarly consider 5+10+15+...+995
here a=5,d=5,l=995 ,find n and then S5
again consider 15+30+45+...+990
here a=15,d=15,l=990,find n and S15
required sum=S3+S5-S15