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7.3 & 7.4 Recursion Formulas & Creating Rules to Define Sequences

7.3 & 7.4 Recursion Formulas & Creating Rules to Define Sequences. What are recursion formulas?. no…. This?!. no…. This?!. FINALLY!. This?!. Recursion formula:. (for real this time) . A formula relating the general term of a sequence to the previous term or terms.

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7.3 & 7.4 Recursion Formulas & Creating Rules to Define Sequences

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  1. 7.3 & 7.4 Recursion Formulas & Creating Rules to Define Sequences What are recursion formulas?

  2. no… This?!

  3. no… This?!

  4. FINALLY! This?!

  5. Recursion formula: (for real this time)  • A formula relating the general term of a sequence to the previous term or terms • Is made up of two parts Equation to calculate other terms, using the first term First term General terms (formulas) are explicit formulas, where you can calculate any term without knowing the previous term in the sequence.

  6. = + t t 3 - 8 8 1 Here is a recursive formula: Notice its two parts! Can you use the formula for tn to find t8? Not really… we need t7 to find t8. Yes & no… we can use a recursive formula with the 1st term given to find the 2nd term, then with that find the 3rd term, then the 4th, etc… So, can we find any term?

  7. Write the first 3 terms of each of the following sequences: #1 Not all sequences will be arithmetic or geometric #2

  8. Write an explicit formula for the sequence determined by the following recursion formula. Geometric, since each term is found by multiplying the previous term by -0.5 (the common ratio) Will the sequence be arithmetic, geometric, or neither?  use…

  9. Is the sequence determined by the following recursion formula arithmetic, geometric, or neither? Please explain. It will be arithmetic, since each new term is found by subtracting 2 from the previous term (ie. there is a common difference).

  10. So, how are explicit and recursion formulas related? arithmetic sequences geometric sequences explicit recursion Add ‘d’ (the common difference) to the previous term. Multiply the previous term by ‘r’ (the common ratio).

  11. What about sequences that are neither geometric nor arithmetic??? Many times you will be given a sequence where the pattern between the numbers is not arithmetic or geometric. When this occurs, often, the pattern can be best described using a recursive formula. Sometimes a general term cannot be found. Let’s take a look at one example…

  12. Fibonacci Sequence Video What recursive formula would represent the Fibonacci Sequence? http://videos.howstuffworks.com/hsw/12113-patterns-and-beauty-striving-for-the-golden-ratio-video.htm t1 = 1, t2 = 1, tn = tn-1 + tn-2

  13. Your Turn! Time to play the Tower of Hanoi!! Tower of Hanoi Puzzle Homework: Please complete the practice questions on the back of the handout

  14. math

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