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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text: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 a
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.
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