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?
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.
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.