Transcript of OBJECTIVES: Determine if a Sequence is Geometric Find a Formula for a Geometric Sequence Find the...
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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)