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Analyze the sequence 1, 8, 17, 100, 494, 1711, 4648, 10697, 21855, 40834, 71171 using sequences...

Analyze the sequence 1, 8, 17, 100, 494, 1711, 4648, 10697, 21855, 40834, 71171 using sequences of differences. (Enter your answers as a comma-separated list of values ordered with respect to increasing n.)

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Answer #1

Given sequence:   1, 8, 17, 100, 494, 1711, 4648, 10697, 21855, 40834, 71171

First difference:       7, 9, 83,   394, 1217, 2937, 6049, 11158, 18979, 30337

Second difference      2,   74, 311, 823, 1720, 3112, 5109, 7821,   11358

Third difference:            72, 237, 512, 897, 1392, 1997, 2712, 3537

Fourth difference:             165, 275, 385, 495, 605,   715, 825

Fifth difference                    110, 110, 110, 110, 110, 110

Since fifth difference is constant, the sequence is of polynomial of degree 5.

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