Question

the sum of three consecutive even number 282. find the three numbers

Answer 1

The three numbers are 93,94,95

Answer 2

The three consecutive even numbers whose sum evaluates to 282 are 92, 94, and 96

What are consecutive numbers?

As the term consecutive implies, the numbers who come one after the other are  called consecutive.

In case of consecutive even numbers, those even numbers who are adjacent to each other.

Example: 2,4,6 are consecutive events but 2,6,12 are not as there are events between 2 and 6 and between 6 and 12, so they are not closest to each other.

Let the first even of those three consecutive numbers whose sum is 282 be denoted by $2n$

Then, we get the rest of the two evens as $2n + 2, 2n+4$

Since their sum is 282, therefore,

$2n + (2n+2) + (2n+4) = 282\\2n +2n + 2n + 2 + 4 = 282\\6n + 6 = 282\\\\\text{Subtracting 6 from both the sides}\\\\6n = 282 - 6 = 276\\\\\text{Dividing both the sides by 6, we get}\\\\n = \dfrac{276}{6} = 46$

Thus, the three consecutive evens whose sum is 282 are:

$2n = 2(46) = 92\\2n + 2 = 94\\2n + 4 = 96$

Therefore, the three consecutive even numbers whose sum evaluates to 282 are 92, 94, and 96

Learn more about consecutive numbers here:

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