Use the simplest rule you can find to calculate the next three terms of the following sequence. 8, 3, 0, –1, 0, . . . a. 0, 0, 0 c. 3, 8, 15 b. –1, 0, 8 d. -3, -6, -8
_____ First differences are the sequence of differences of the given numbers: .. 3 -8 = -5 .. 0 -3 = -3 .. -1 -0 = -1 .. 0 -(-1) = 1 Second differences are the sequence of differences of these: .. -3 -(-5) = 2 .. -1 -(-3) = 2 .. 1 -(-1) = 2 All of these are 2, so the sequence can be described by a *second* order polynomial (because *second* differences are a non-zero constant).
