Consecutive numbers follow one right after the other. An example of three consecutive numbers is 17, 18, and 19. Another example is -100, -99, -98. Choose any set of three consecutive numbers. Find their average. What do you notice? Find the average of another set of three consecutive numbers. What do you notice? Explain why the thing you noticed must always work, or find a counterexample.

First, find the average of the given examples. Note that, when finding the average, you add all the numbers in the given set, and divide by the amount of terms in that set.

So in the case of the three consecutive numbers 17, 18, 19, the average number would be found by adding all the terms and dividing by 3:

(17 + 18 + 19)/3 = (54)/3

(54)/3 = 18

Next, solve the other given example. The three given consecutive numbers are -100, -99, -98. Add the terms together and divide by 3:

(-100 + -99 + -98)/3 = (-100 - 99 - 98)/3 = (-297)/3 = -99

What can be noticed is that, when solving for the average of three consecutive numbers, the average would be the second term given in that set.

The rule will always work, as the answer follows within a linear path (when graphed). Average, as defined in math, is a calculated "central" value of a set of numbers. The central number in a given set of three consecutive numbers will always be the middle term. Therefore, the rule is always applicable with a set of three consecutive numbers.

Learn more about finding the average, here:

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