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You mean what IS a geometric sequence?

It's when the ratio of the terms is constant, meaning:

1, 2, 4, 8, 16...

The ratio of one term to the term directly following it is always 1:2, or .5.

So like, instead of an arithmetic sequence, where you're adding a specific amount each time, in a geometric sequence, you're multiplying by that term.

Q: What does geometric sequence?

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

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?

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

A single number does not constitute a sequence.

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No.

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

a sequence of shifted geometric numbers

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.

antonette taño invented geometric sequence since 1990's

A descending geometric sequence is a sequence in which the ratio between successive terms is a positive constant which is less than 1.

what is the recursive formula for this geometric sequence?

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

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.

A single number does not constitute a sequence.