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OBJECTIVES: Determine if a Sequence is Geometric Find a Formula for a Geometric Sequence Find the Sum of a Geometric Sequence Find the Sum of a Geometric Series

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* A sequence in which each term after the first is obtained by multiplying the preceding term by a fixed nonzero constant. The amount by which we multiply each time is called the common ratio of the sequence. * Common Ratio, r, is found by dividing any term after the first term by the term that directly precedes it. * General Term of a Geometric Sequence: the nth term (the general term) of a geometric sequence with first term and common ratio * Explicit Formula: * Recursive Formula:

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* EX 1: Find the common ratio and write out the first four terms of the geometric sequence

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* EX 2: Find the nth term of the geometric sequence whose initial term and common ratio are given. What is the fifth term?

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* EX 3: Find the eighth term of the geometric sequence whose first term is -4 and whose common ratio is -2

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* EX 4: Determine the type of sequence A) B) C)

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* The sum of the first terms of a geometric sequence is given by: In which is the first term and is the common ratio

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* EX 5: Find the sum of the first 18 terms of the geometric sequence:

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* A) * B)

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* If, then the sum of the infinite geometric series in which is the first term and is the common ratio is given by: If, then the infinite series does not have a sum

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* A) * B)