by The Open University
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We've seen examples in Section 2 where the quantities in problems are always related in a particular way. For example, V = u + at is a general expression connecting initial and final velocity (u and V), constant acceleration (a) and time (t). This single formula allows you to calculate final velocity, V, for any values of u, a and t, not just for one specific set of data. Algebra enables us to generalise ? something may seem to be true for many sets of specific data values, but is it true for all such sets?
Before discussing equations in more detail, we would like to show you what we mean.
Find the sum of three consecutive whole numbers or integers. Divide your answer by 3. What do you notice? (You may need to try this for several sets until you find a pattern.)
We can explain this by working out a formula for this sum. Suppose we call the first number n, what will the second and third numbers be? What will their sum be, in terms of n? Can you now explain the result?
The three consecutive numbers are n, (n + 1), and (n + 2). If you add these together, you get n + (n + 1) + (n + 2) = 3n + 3.
Dividing by 
Therefore, the product of three consecutive numbers is always divisible by three.
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