In simpler terms, a geometric sequence is a sequence in which some constant (same) number multiplies every-time to give u the next number in the sequence.
2, 4, 6, 8, 10, 12 - The constant is 2 (E.g. 2 x 2 = 4)
6, 36, 216, 1296, 7776 - The constant is 6 (E.g. 6 x 6 = 36)
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To figure out the constant number we just divide one number in the sequence by the one next to it on the left.
E.g. 36/6 = 6
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That first example, starting at 2 with a constant=2, is arithmetical not geometrical because it simply adds 2 each time. If the constant is a multiplier the series is 2, 4, 8, 16, 32, 64, ...
No.
a sequence of shifted geometric numbers
A descending geometric sequence is a sequence in which the ratio between successive terms is a positive constant which is less than 1.
No.
A geometric sequence is : a•r^n which is ascending if a is greater than 0 and r is greater 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
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.