When doing algebra problems, sometimes we are asked to prove something is true for an even number or that something is true for an odd number. The “something” we are trying to prove may only be true for even numbers and not necessarily true for odd numbers. So how to we represent even numbers in algebra? Well, what does it mean to be an even number? It means that the number is divisible by 2. So if a question asks us about an even number, we can represent it by 2n.
We usually think of odd numbers as being defined as “not divisible by 2” or just “any number that isn’t even”. Well, we can be a bit more precise and say that odd numbers are numbers that are 1 greater than an even number. So they can be represented as 2n+1 . If you wanted, you could instead say that odd numbers are the numbers that are 1 less than even numbers. In that case, you would use 2n-1 . Either form will get you the right answer.
Now you're ready to try a few!
Click on the PDF for sample questions.
Click on the PDF for the solutions.
