Question

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

Answer 1

Rule: second differences are 2.

Selection C is appropriate.

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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).