Question

An even integer can be represented by the expression 2n, where n is any integer. Find three consecutive even integers that have a sum of 54. The three consecutive even integers, in order from least to greatest, are , , and . Explain your reasoning. Expressions for the next two consecutive even integers after 2n are and . Solving the equation =54, and substituting the solution into the expressions for the three integers results in the three integers given above.

Answer 1

As consecutive odd numbers differ by two (example: 3, 5, 7), the first odd number can be expressed as 2n + 1, the next can be found by adding two to the first to get 2n + 1 + 2 which simplifies to 2n + 3. Finally the expression for the third consecutive odd integer can be found by adding two to the previous, 2n + 3, to get 2n + 5. Adding these three together and setting them equal to your sum gets the equation

2n + 1 + 2n + 3 + 2n + 5 = 63

Combine like terms and solve For n.

Once you have n, you must substitute it back into your three expressions (2n + 1, 2n + 3, 2n + 5) to find the three odd integers.

Hope this helps :)