Question #42fa8

1 Answer
yumean1119
Dec 13, 2017

The sum is #35392#.

Explanation:

The numbers divisible by #2# and #7# are multiples of #14#.
Use the sum of an arithmetic progression
#S=1/2n(a+l)#.
#S#: sum
#n#: number of terms
#a#: first term
#l#: last term

The least 3-digit number divisible by #14# is #14*8=112#, and the greatest 3-digit multiple of #14# is #14*71=994#.
And, there are #71-8+1=64# multiples of #14# between #112# and #994#.

So, the sum is
#S=1/2*64*(112+994)=35392#.

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