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Geometric Sequences. Geometric Sequences. A sequence which has a constant ratio between terms. The rule is exponential . Example: 4, 8, 16, 32, 64, … (generator is x2). x2. Discrete. x2. x2. 0 1 2 3 4 5 6. x2. Working Backwards for a Rule.

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## Geometric Sequences

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**Geometric Sequences**A sequence which has a constant ratio between terms. The rule is exponential. Example: 4, 8, 16, 32, 64, … (generator is x2) x2 Discrete x2 x2 0 1 2 3 4 5 6 x2**Working Backwards for a Rule**First find the generator and the n=0 term. Then write the equation: Ex: 0 1 2 3 4 3, 15, 75, 375, … x5 Sequences start with n=1 now! t(0) is not in the sequence! Do not include it in tables or graphs!**Positive Multipliers**In a geometric sequence, if the multiplier is: • Less than one but greater than 0 (0<b<1) • Equal to 1 (b=1) • Greater than 1 (b>1) The sequence decreases. The sequence is constant. The sequence increases.**Example of a Sequence**2, 6, 18, 54, ___, ___, … Generator: Representations Table: Rule: 486 162 Multiply by 3 t(n) = 2/3(3)n**Example of a Sequence**625, 125, 25, 5, ___, ___, … Generator: Representations Table: Rule: 0.2 1 Multiply by 1/5 (0.2) t(n) = 3125(0.2)n**Sequences v Functions**Sequence: t(n) Function: f(x) Domain (n) = Positive Integers (sometimes 0) Range (t(n)) = Can be all Real numbers The Graph is Discrete Domain (x) = Can be all Real numbers Can be all Real numbers Range (f(x))= The Graph can be Continuous

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