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Essential Question: What is a sequence and how do I find its terms and sums?

Essential Question: What is a sequence and how do I find its terms and sums?. How do I find the sum & terms of geometric sequences and series?. Geometric Sequences. Geometric Sequence – a sequence whose consecutive terms have a common ratio. Geometric Sequence.

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Essential Question: What is a sequence and how do I find its terms and sums?

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  1. Essential Question: What is a sequence and how do I find its terms and sums? How do I find the sum & terms of geometric sequences and series?

  2. Geometric Sequences Geometric Sequence– a sequence whose consecutive terms have a common ratio.

  3. Geometric Sequence A sequence is geometric if the ratios of consecutive terms are the same. The number r is the common ratio.

  4. Ex. 1 Are these geometric? Yes 2n 2, 4, 8, 16, …, formula?, … Yes 4(3)n 12, 36, 108, 324, …, formula?,… No (-1)n /3 1, 4, 9, 16, …, formula?, … No n2

  5. Finding the nth term of a Geometric Sequence an = a1rn – 1

  6. Ex. 2b Write the first five terms of the geometric sequence whose first term is a1 = 9 and r = (1/3).

  7. Ex. 3 Find the 15th term of the geometric sequence whose first term is 20 and whose common ratio is 1.05 an = a1rn – 1 a15 = (20)(1.05)15 – 1 a15 = 39.599

  8. Ex. 4 Find a formula for the nth term. 5, 15, 45, … an = a1rn – 1 an = 5(3)n – 1 What is the 9th term? an = 5(3)n – 1 a9 = 5(3)8 a9 = 32805

  9. sum of a finite geometric series

  10. Ex. 6 Find the sum of the first 12 terms of the series 4(0.3)n = 4(0.3)1 + 4(0.3)2 + 4(0.3)3 + … + 4(0.3)12 = 1.714

  11. Ex. 7 Find the sum of the first 5 terms of the series 5/3 + 5 + 15 + … r = 5/(5/3) = 3 = 605/3

  12. What are your questions? Homework: Page 771 #16-22 even, 26, 27, 30, 32, 37, 38

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