What is a geometric sequence?

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answers:
Krishnamurthy say: In a Geometric Sequence each term is found by multiplying the previous term by a constant.
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Jeffrey K say: Each term is multiplied by some number to get the next term. That number must be the same number for every term in the sequence.
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sepia say: In a Geometric Sequence each term is found by multiplying the previous term by a constant. In General we write a Geometric Sequence like this:{a, ar, ar2, ar3, ... }where: 1. a is the first term, and 2. r is the factor between the terms (called the "common ratio") But be careful, r should not be 0: 1. When r=0, we get the sequence {a,0,0,...} which is not geometric
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Shane say: A geometric sequence is a series of numbers that change on a multiplicative scale (that is, they are multiplied in a pattern).
For example, the sequence 1, 2, 4, 8, 16, 32, ... is a geometric sequence.

Geometric sequences can usually be expressed as a constant plus or minus another constant to the power of n, where n might start at 0 or 1 depending on your preferred method.
For example, the above sequence can be written as s = 0 + 2^n, where n starts at 0, or as s = 2^n-1, where n starts at 1.
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Captain Matticus, LandPiratesInc say: Terms that share a common ratio between them

1 , 2 , 4 , 8 , 16 , 32 , 64 , 128 , ....

Each successive term is twice the previous term.

3 , 6 , 12 , 24 , 48 , 96 , 192 , 384 , ...

Again, each successive term is twice the previous term. Other ratios are obviously possible:

1 , 1 , 1 , 1 , 1 , 1 , ...

Each term is the product of the previous term and 1

10 , 100 , 1000 , 10000 , ....

Each term is ten times the previous term.

And so on.
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ted s say: a mathematical sequence where the ratio between consecutive term is constant
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edxoc say: mwaekkkw
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