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Jimboslice

  • 2 years ago

The following function defines a recursive sequence. f(0) = -5 f(1) = 20 f(n) = -4•f(n -1) - 3•f(n - 2); for n > 1 Which of the following sequences is defined by this recursive function? -5, -20, -65, -200, … -5, 20, -92, 372, … -5, -24, -92, -372, … -5, 20, -65, 200, …

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  1. amistre64
    • 2 years ago
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    what is the first term?

  2. Jimboslice
    • 2 years ago
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    f(0) = -5 ?

  3. amistre64
    • 2 years ago
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    yes, so they give you the first one what is the second term?

  4. amistre64
    • 2 years ago
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    we can narrow the options by eliminating the ones that have the wrong first and second terms, then the third term gets us to only one option that fits

  5. amistre64
    • 2 years ago
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    we can use the rule given to determine f(2) f(n) = -4•f(n -1) - 3•f(n - 2) f(2) = -4•f(2 -1) - 3•f(2 - 2) f(2) = -4•f(1) - 3•f(0) ^^ ^^ we already know these values to plug into the rule

  6. Jimboslice
    • 2 years ago
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    ok so what now ?

  7. amistre64
    • 2 years ago
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    that IS the "what now" you work it out

  8. amistre64
    • 2 years ago
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    or you ask questions about what it is you dont understand

  9. Jimboslice
    • 2 years ago
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    oh ok hold on

  10. Jimboslice
    • 2 years ago
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    i dont get what im suppose to work out ....

  11. amistre64
    • 2 years ago
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    f(n) = -4•f(n -1) - 3•f(n - 2) f(2) = -4•f(2 -1) - 3•f(2 - 2) f(2) = -4•f(1) - 3•f(0) ^^ ^^ we already know these values to plug into the rule

  12. amistre64
    • 2 years ago
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    f(0) = -5 f(1) = 20

  13. amistre64
    • 2 years ago
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    wherever you see f(0), replace it by -5 wherever you see f(1), replace it by 20

  14. Jimboslice
    • 2 years ago
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    what if i see f(2)

  15. amistre64
    • 2 years ago
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    f(2) is what we are calculating ... f(2) will equal ______________

  16. Jimboslice
    • 2 years ago
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    f(2) = -4•f(1) - 3•f(0) =-65 correct?

  17. amistre64
    • 2 years ago
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    very good :)

  18. amistre64
    • 2 years ago
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    so what we are looking for is a sequence that starts out: f(0), f(1), f(2) -5, 20, -65 only one of the options starts out like this

  19. Jimboslice
    • 2 years ago
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    the last one ..

  20. amistre64
    • 2 years ago
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    correct

  21. Jimboslice
    • 2 years ago
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    thank you very much for explaining

  22. amistre64
    • 2 years ago
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    good luck :)

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