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 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?
To determine if a sequence is geometric, check if the ratio between consecutive terms is constant. You can calculate the ratio by dividing each term by the preceding term. If this ratio remains the same for all pairs of consecutive terms, then the sequence is geometric. Additionally, a geometric sequence can be verified using a geometric sequence calculator, which will confirm the common ratio and provide further analysis.
It is called arithmetico-geometric sequence. I have added a link with some nice information about them.
A descending geometric sequence is a sequence in which the ratio between successive terms is a positive constant which is less than 1.
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
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.