Question: x +14 3 ( - 1) Discovery Precalculus: A Creative and Connected Approach Exploration 1.4.2: Triangular Differences Involving Sequences of the Form f (n) =

 x +14 3 ( - 1) Discovery Precalculus: A Creative and

x +14 3 ( - 1) Discovery Precalculus: A Creative and Connected Approach Exploration 1.4.2: Triangular Differences Involving Sequences of the Form f (n) = ank Take a look at the sequence of square numbers listed in the first row of numbers below. The first several terms of the sequence are listed and, below that, the first differences of the two numbers immediately above, and below that are the differences of the differences (i.e., the second differences). CO 81... m LO m 17... N N Notice that for the sequence n the second differences are all 2. 1. Now explore the differences for the sequence of cubes n3 . Do you notice any patterns

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