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Q: Descending geometric sequence

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No.

a sequence of shifted geometric numbers

No.

A geometric sequence is : a•r^n which is ascending if a is greater than 0 and r is greater than 1.

The sequence 216 12 23 is neither arithmetic nor geometric.

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No.

A geometric sequence is a sequence where each term is a constant multiple of the preceding term. This constant multiplying factor is called the common ratio and may have any real value. If the common ratio is greater than 0 but less than 1 then this produces a descending geometric sequence. EXAMPLE : Consider the sequence : 12, 6, 3, 1.5, 0.75, 0.375,...... Each term is half the preceding term. The common ratio is therefore ½ The sequence can be written 12, 12(½), 12(½)2, 12(½)3, 12(½)4, 12(½)5,.....

Yes, that's what a geometric sequence is about.

a sequence of shifted geometric numbers

antonette taño invented geometric sequence since 1990's

A geometric sequence is : a•r^n while a quadratic sequence is a• n^2 + b•n + c So the answer is no, unless we are talking about an infinite sequence of zeros which strictly speaking is both a geometric and a quadratic sequence.

what is the recursive formula for this geometric sequence?

No.

It is called arithmetico-geometric sequence. I have added a link with some nice information about them.

A geometric sequence is : a•r^n which is ascending if a is greater than 0 and r is greater than 1.

The sequence 216 12 23 is neither arithmetic nor geometric.

=3

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