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12.3 – Geometric Sequences and Series

12.3 – Geometric Sequences and Series. Arithmetic Series. Geometric Series. Sum of Terms. Sum of Terms. Arithmetic Sequences. Geometric Sequences. ADD To get next term. MULTIPLY To get next term. Vocabulary of Sequences (Universal). Find the next three terms of 2, 3, 9/2, ___, ___, ___.

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12.3 – Geometric Sequences and Series

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  1. 12.3 – Geometric Sequences and Series

  2. Arithmetic Series Geometric Series Sum of Terms Sum of Terms Arithmetic Sequences Geometric Sequences ADD To get next term MULTIPLY To get next term

  3. Vocabulary of Sequences (Universal)

  4. Find the next three terms of 2, 3, 9/2, ___, ___, ___ 3 – 2 vs. 9/2 – 3… not arithmetic

  5. 1/2 x 9 NA 2/3

  6. The two geometric means are 6 and -18, since –2, 6, -18, 54 forms an geometric sequence Find two geometric means between –2 and 54 -2, ____, ____, 54 -2 54 4 NA x

  7. -3, ____, ____, ____

  8. x 9 NA

  9. x 5 NA

  10. *** Insert one geometric mean between ¼ and 4*** *** denotes trick question 1/4 3 NA

  11. 1/2 7 x End Day One

  12. 1, 4, 7, 10, 13, …. No Sum Infinite Arithmetic Finite Arithmetic 3, 7, 11, …, 51 Finite Geometric 1, 2, 4, …, 64 1, 2, 4, 8, … Infinite Geometric r > 1 r < -1 No Sum Infinite Geometric -1 < r < 1

  13. Find the sum, if possible:

  14. Find the sum, if possible:

  15. Find the sum, if possible:

  16. Find the sum, if possible:

  17. Find the sum, if possible:

  18. 50 40 40 32 32 32/5 32/5 The Bouncing Ball Problem – Version A A ball is dropped from a height of 50 feet. It rebounds 4/5 of it’s height, and continues this pattern until it stops. How far does the ball travel?

  19. 100 100 75 75 225/4 225/4 The Bouncing Ball Problem – Version B A ball is thrown 100 feet into the air. It rebounds 3/4 of it’s height, and continues this pattern until it stops. How far does the ball travel?

  20. UPPER BOUND (NUMBER) SIGMA (SUM OF TERMS) NTH TERM (SEQUENCE) LOWER BOUND (NUMBER)

  21. Rewrite using sigma notation: 16 + 8 + 4 + 2 + 1 Geometric, r = ½

  22. Rewrite using sigma notation: 19 + 18 + 16 + 12 + 4 Not Arithmetic, Not Geometric 19 + 18 + 16 + 12 + 4 -1 -2 -4 -8

  23. Rewrite the following using sigma notation: Numerator is geometric, r = 3 Denominator is arithmetic d= 5 NUMERATOR: DENOMINATOR: SIGMA NOTATION:

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