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Geometric Sequence

Geometric Sequence. Sequences and Series. Geometric Sequence. A sequence is geometric if the ratios of consecutive terms are the same. 2, 8, 32, 128, 512,. geometric sequence. The common ratio , r , is 4. Find the common ratio of the following:. 1) 1, 2, 4, 8, 16, ... r = 2

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Geometric Sequence

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  1. Geometric Sequence • Sequences and Series

  2. Geometric Sequence Asequence is geometric if the ratios of consecutive terms are the same. 2, 8, 32, 128, 512, . . . geometric sequence The common ratio, r, is 4.

  3. Find the common ratio of the following: • 1) 1, 2, 4, 8, 16, ... • r = 2 • 2) 27, 9, 3, 1, 1/3, ... • r = 1/3 • 3) 3, 6, 12, 24, 48, ... • r = 2 • 4) 1/2, -1, 2, -4, 8, ... • r = -2

  4. Write the first 6 terms of the geometric sequence with the first term of 6 and common ratio of 1/3

  5. a2 = 15(5) a3 = 15(52) a4 = 15(53) The nth term of a geometric sequence has the form an = a1rn - 1 where r is the common ratio of consecutive terms of the sequence. a1 = 15 15, 75, 375, 1875, . . . The nth term is 15(5n-1).

  6. Example Find the 9th term of the geometric sequence 7, 21, 63, . . . a1 = 7 an = a1rn – 1 = 7(3)n – 1 a9 = 7(3)9 – 1 = 7(3)8 = 7(6561) = 45,927 6 The 9th term is 45,927.

  7. Your Turn Find the 8th term of the geometric sequence whose first term is -4 and whose common ratio is -2 a8 = -4(-128) = 512

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