Education Quality and Accountability Office (EQAO) Grade 9 Practice Exam

The main idea is about how a sequence changes from one term to the next. The first difference is found by subtracting each term from the term that comes after it, so you get a new sequence that shows the step-by-step changes between consecutive terms. This lets you see whether the sequence increases by a constant amount or how that amount itself changes. For example, in a sequence like 2, 5, 9, 14, the differences are 3, 4, 5, which shows the change from term to term isn’t constant. If the differences were all the same, the original sequence would be arithmetic, meaning it adds the same amount each time.

The other ideas aren’t measuring the same thing: multiplying consecutive terms gives a product, not the change between terms; adding all terms gives a total sum, not the step-by-step change; and taking the ratio of consecutive terms gives the relative growth factor, which is used for geometric sequences, not the first difference.