2006-08-13 04:59:37 · 1 answers · asked by altgrave 4 in Education & Reference ➔ Higher Education (University +)
SIMPLE LANGUAGE!
2006-08-19 08:48:31 · update #1
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geometric (logarithmic) progression
n.
A sequence, such as the numbers 1, 3, 9, 27, 81, in which each term is multiplied by the same factor in order to obtain the following term. Also called geometric sequence.
In mathematics, a sequence of numbers in which each number is obtained from the previous one by multiplying by a constant. For example, the sequence 1, 2, 4, 8, 16, 32 ... (in which each number is multiplied by 2 to get the next one) is a geometric progression.
# Many processes involving growth and spreading, such as population increases, can be described as geometric progressions.
Examples
A sequence with a common ratio of 2 and a scale factor of 1 is
1, 2, 4, 8, 16, 32, ....
A sequence with a common ratio of 2/3 and a scale factor of 729 is
729 (1, 2/3, 4/9, 8/27, 16/81, 32/243, 64/729, ....) = 729, 486, 324, 216, 144, 96, 64, ....
A sequence with a common ratio of −1 and a scale factor of 3 is
3 (1, −1, 1, −1, 1, −1, 1, −1, 1, −1, ....) = 3, −3, 3, −3, 3, −3, 3, −3, 3, −3, ....
This sequence's behaviour depends on the value of the common ratio.
If the common ratio is:
* Positive, the terms will all be positive.
* Negative, the terms will alternate between positive and negative.
* 0, the results will remain at zero.
* Greater than 1, there will be exponential growth towards infinity (positive).
* 1, the progression is a constant sequence.
* Between 1 and −1 but not zero, there will be exponential decay towards zero.
* −1, the progression is an alternating sequence (see alternating series)
* Less than −1, there will be exponential growth towards infinity (positive and negative).
2006-08-19 02:46:01 · answer #1 · answered by --- 6 · 0⤊ 0⤋