The sum of three consecutive even numbers is 318. What is the 1st number?

x+x+2+x+4=318

3x+6=318

3x=312

x=104

The first number is 104.

Step-by-step explanation:

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

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

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step-by-step explanation: