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12.3 – Analyze Geometric Sequences and Series

12.3 – Analyze Geometric Sequences and Series. Geometric Sequence:. Ratio of any term to the previous term is constant. Common Ratio:. Ratio each term is increasing by. 1. Tell whether the sequence is geometric. 4, 10, 18, 28, 40, …. 5 2. 9 5. 14 9. 10 7. No.

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12.3 – Analyze Geometric Sequences and Series

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  1. 12.3 – Analyze Geometric Sequences and Series

  2. Geometric Sequence: Ratio of any term to the previous term is constant Common Ratio: Ratio each term is increasing by

  3. 1. Tell whether the sequence is geometric. 4, 10, 18, 28, 40, … 5 2 9 5 14 9 10 7 No

  4. 2. Tell whether the sequence is geometric. 625, 125, 25, 5, 1, … 1 5 1 5 1 5 1 5 Yes

  5. 3. Tell whether the sequence is geometric. –4, 8, –16, 32, –64, … –2 –2 –2 –2 Yes

  6. Rule for a Geometric Sequence: The nth term of a geometric sequence with first term a1 and common ratio r is given by:

  7. Write a rule for the nth term of the sequence. Then find a7. a1 = 4 4, 20, 100, 500, …. r = 5 a7 = 4(5)7–1 a7 = 4(5)6 a7 = 4(15625) a7 = 62500

  8. 5. Write a rule for the nth term of the sequence. Then find a7. a1 = 152 152, –76, 38, –19, … -1 2 r = a7 = 152(-1/2)7–1 a7 = 152(-1/2)6 a7 = 152(1/64) a7 = 19/8

  9. 6. Write a rule for the nth term of the geometric sequence, given: a4 = 12, r = 2 12 = a1(2)4 – 1 12 = a1(2)3 12 = 8a1 3/2 = a1

  10. 7. Write a rule for the nth term of the geometric sequence, given: a6 = –96, r = 2/3

  11. 8. Write a rule for the nth term of the geometric sequence, given: a3 = –48, a6 = 3072 r3

  12. 9. Write a rule for the nth term of the geometric sequence, given: a2 = –12, a4 = –3 r2

  13. Sum of a Finite Geometric Series: The sum of the first n terms of a geometric series with common ratio r 1 is:

  14. 10. Find the sum of the geometric series. a1 = 4(3)1-1 = 4(1) = 4 r = 3 n = 16

  15. 11. Find the sum of the geometric series. a1 = 12(-1/2)0 = 12(1) = 12 r = -1/2 n = 8

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