Geometric Sequence A sequence like 3, 9, 27, 81,, where the
ratio between consecutive terms is a constant, is called a
geometric sequence. In a geometric sequence, the first term t1, is
denoted as a. Each term after the first is found by multiplying a
constant, called the common ratio, r, to the preceding term. The
list then becomes. {a, ar, ar 2, ar 3,...}
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Geometric Sequences Formulas In general: {a, ar, ar 2, ar
3,...,ar n-1,...}
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Example 1 Finding Formula for the nth term In the geometric
sequences: {5, 15, 45,...}, find a) b) c) n n a) 5 5 b) 10 c) n
n
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Example 2 Finding Formula for the nth term Given the geometric
sequence: {3, 6, 12, 24,...}. a) Find the term b) Which term is
384? n n a) 14 b) We know the n th term is 384 !! Drop the
bases!!
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Example 3 Find the terms in the sequence In a geometric
sequence, t 3 = 20 and t 6 = -540. Find the first 6 terms of the
sequence. (2) (1) (1)(2) Substitute into (1) Therefore the first 6
terms of the sequences are:
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Example 4 Find the terms in the sequence In a geometric
sequence, t 3 = 20 and t 6 = -540. Find the first 6 terms of the
sequence. METHOD 2 t n=20r (n-3) t 1 = 20r (1-3) To find a, we use
the same thinking process!! Therefore the first 6 terms of the
sequences are:
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Example 5 Applications of Geometric sequence Determine the
value of x such that Form a geometric sequence. Find the sequences
and Therefore the sequences are: 5+4, 2(5)+5, 4(5)+5,... 9, 15,
25,...
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Homework: Check the web site Course Pack: Applications of
Sequences
