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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,...}

Geometric Sequences Formulas In general: {a, ar, ar 2, ar 3,...,ar n-1,...}

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

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!!

Example 3 – Find the terms in the sequence In a geometric sequence, t 3 = 20 and t 6 = Find the first 6 terms of the sequence. (2) (1) (1)(2) Substitute into (1) Therefore the first 6 terms of the sequences are:

Example 4 – Find the terms in the sequence In a geometric sequence, t 3 = 20 and t 6 = 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:

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,...

Homework: Check the web site Course Pack: Applications of Sequences