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Answer:
x+x+2+x+4=318
3x+6=318
3x=312
x=104
The first number is 104.
Step-by-step explanation:
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Explanation:
n = some integer
2n = some even integer
2n+2 = next integer after 2n
2n+4 = next integer after 2n+2
The sequence {2n, 2n+2, 2n+4} represents three consecutive even integers. One follows right after another. A more concrete example of consecutive even integers could be something like {2,4,6} or {8,10,12}. The goal is to find which set like this has their numbers add to 318.
We could guess-and-check our way to the answer. In other words, use trial and error. However, a much more efficient way is to use algebra.
Let's add up the three number expressions of 2n, 2n+2, and 2n+4 to get
(2n)+(2n+2)+(2n+4) = (2n+2n+2n) + (2+4) = 6n+6
The three numbers add to 6n+6
This sum must be 318. Let's set 6n+6 equal to 318 and solve for n
6n+6 = 318
6n = 318-6
6n = 312
n = 312/6
n = 52
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If n = 52, then,
Note the sequence 104, 106, 108 are all even numbers where they follow right after one another. This shows they are consecutive even numbers.
Furthermore, note how,
104+106+108 = 318
which confirms our answer