When you solve questions like "The sum of 3 consecutive integers is 147. Find the integers." do you find consecutive even integers and consecutive odd integers the same way?

consecutive integers are one unit apart,

so 3 of them would be x, x+1, and x+2

both even or odd consecutive integers are 2 units apart,
you would define 3 of them as x, x+2, x+4

whether you x comes out as either even or odd will depend on the sum that is given.

the sum of 3 even consecutive numbers are always even, while the sum of 3 consecutive odd numbers will always be odd.

thanks

Yes, finding consecutive even integers and consecutive odd integers follow a similar approach.

To find consecutive even integers, you need to understand that consecutive even integers have a difference of 2 between each integer. So, if the first even integer is represented by "x," the next consecutive even integer would be "x + 2," and the one after that would be "x + 4," and so on.

On the other hand, to find consecutive odd integers, you also start with an initial odd integer represented by "x." The next consecutive odd integer would then be "x + 2," followed by "x + 4," and continues with a difference of 2 between each integer.

When solving a problem like "The sum of 3 consecutive integers is 147," you can use algebraic equations to represent the situation. Let's assume the first integer is represented by "x." For consecutive even integers, the second and third consecutive integers would be "x + 2" and "x + 4," respectively. For consecutive odd integers, they would be "x + 2" and "x + 4" as well.

Consequently, the equation representing the sum of the three consecutive integers can be written as:

x + (x + 2) + (x + 4) = 147

After simplifying and solving the equation, you can find the value of "x" or the initial integer. Depending on whether you are looking for consecutive even or odd integers, you can then find the subsequent integers using the formulas mentioned earlier.

In summary, while the methodology for finding consecutive even and odd integers is the same, the key difference lies in the starting point, where even integers always have a difference of 2, while odd integers also have the same difference.