Question #42fa8

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Question #42fa8

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Answer 1 · 2017-12-13T01:41:10

The sum is $35392$ $35392$ .

Explanation:

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

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

So, the sum is
$S = \frac{1}{2} \cdot 64 \cdot (112 + 994) = 35392$ $S=1/2*64*(112+994)=35392$ .

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Question #42fa8

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