The statements below all relate to polynomial sequences. Select all the statements which are TRUE. Every geometric sequence is also a polynomial sequence. Every constant sequence is an arithmetic sequence, a geometric sequence, and as polynomial sequence. The sequence with closed formula an-A(n-1)3+B(n-1)+C has constant third differences equal to 3A. The sequence with closed formula an-A(n-1)2+B(n-1)+C has constant first differences equal to 2A. If a sequence has non-zero constant nth differences, then its closed formula is a degree n polynomial. Every sequence with constant second differences is itself the sequence of first differences of a cubic sequence. If a sequence has constant nth differences, then all differences thereafter are also constant. Every arithmetic sequence is also a polynomial sequence.

The statements below all relate to polynomial sequences. Select all the statements which are TRUE. Every geometric sequence is also a polynomial sequence. Every constant sequence is an arithmetic sequence, a geometric sequence, and as polynomial sequence. The sequence with closed formula an-A(n-1)3+B(n-1)+C has constant third differences equal to 3A. The sequence with closed formula an-A(n-1)2+B(n-1)+C has constant first differences equal to 2A. If a sequence has non-zero constant nth differences, then its closed formula is a degree n polynomial. Every sequence with constant second differences is itself the sequence of first differences of a cubic sequence. If a sequence has constant nth differences, then all differences thereafter are also constant. Every arithmetic sequence is also a polynomial sequence.

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter9: Sequences, Probability And Counting Theory

Section9.3: Geometric Sequences

Problem 51SE: Use recursive formulas to give two examples of geometric sequences whose 3rd terms are 200.

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