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anonymous

  • one year ago

Find the first four terms of a squence using the recursive definition. f(1)=6, f(n)=f(n-1)-5

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  1. amistre64
    • one year ago
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    what does the definition tell us?

  2. anonymous
    • one year ago
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    Using a process that can be repeated. So like the arithmetic sequence. The arithmetic sequence is adding a constant of the previous term.

  3. amistre64
    • one year ago
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    ok, in this case, what are we 'adding' to one term to make the next term? any ideas?

  4. amistre64
    • one year ago
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    or if we simply let n={1,2,3,4} and the rule defined, we get: f(1) = 6 f(2) = f(1) -5 f(3) = f(2) -5 f(4) = f(3) -5

  5. amistre64
    • one year ago
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    so, what would our 4 terms be?

  6. anonymous
    • one year ago
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    So since its asking for the first four terms wouldnt it be f(1)=6 f(n)=f(n-1)-5 f(2)=f(2-1)-5=f(1)+1= 6+1=7 so 7 would be one of the four terms but I dont know how to get the rest.

  7. amistre64
    • one year ago
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    f(2) = f(2-1) - 5 f(2) = f(1) - 5 f(2) = 6 - 5 = 1, not 7 so, f(1) = 6, f(2) = 1 ---------------------- now repeat with n=3 f(3) = f(3-1) - 5 f(3) = f(2) - 5 f(3) = 1 - 5 = -4 so, f(1) = 6, f(2) = 1, f(3) = -4 what is f(4) ?

  8. amistre64
    • one year ago
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    as we find each new term, we can use it to find the next one .... hence the naming it: 'recursive'

  9. amistre64
    • one year ago
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    f(4) = f(4-1) - 5 f(4) = f(3) - 5 ^^^ but we know f(3) = -1 f(4) = -1 - 5

  10. amistre64
    • one year ago
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    pfft, f(3) = -4 .... these tired old eyes play tricks on me

  11. amistre64
    • one year ago
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    can you tell me how we are working this? its basic to me so i cant really see the difficulty. you have to tell me what it is that is confusing you

  12. anonymous
    • one year ago
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    Oka, I understand but im confused on f(4)

  13. amistre64
    • one year ago
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    ok, tell me how you are looking at f(4) show me your working

  14. amistre64
    • one year ago
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    if you know how to get from f(1) to f(2), then the process does not change. f(2) allows us to get f(3), and f(3) allows us to get f(4). typing errors aside, its pretty repetitive.

  15. anonymous
    • one year ago
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    So f(4)=-6?

  16. amistre64
    • one year ago
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    f(4) = f(3) - 5 f(3) = -4 [i mistyped it before as -1] f(4) = -4 -5

  17. amistre64
    • one year ago
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    another way to look at it, just subtract 5 from the setup before ... f(1) = 6 f(2) = 6-5 f(3) = 6-5-5 f(4) = 6-5-5-5

  18. anonymous
    • one year ago
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    So f(4)=-9

  19. amistre64
    • one year ago
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    yes

  20. amistre64
    • one year ago
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    now, what are our 4 terms?

  21. anonymous
    • one year ago
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    1,-5,-4,-9

  22. amistre64
    • one year ago
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    f(1) = 6 f(2) = 6-5 = 1 f(3) = 6-5-5 = -4 f(4) = 6-5-5-5 = -9

  23. anonymous
    • one year ago
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    oh im sorry I didnt mean to write -5 but thank you so much

  24. amistre64
    • one year ago
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    \[\begin{pmatrix}n\\f(n)\end{pmatrix}=\begin{pmatrix}1&2&3&4\\6&1&-4&-5\end{pmatrix}\]

  25. amistre64
    • one year ago
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    good luck :)

  26. amistre64
    • one year ago
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    yeah, 6, 1 -4, -9 math and typing dont mix that well

  27. anonymous
    • one year ago
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    I agree on that ,Do you think you can help me with a couple more?

  28. amistre64
    • one year ago
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    maybe one more; its late (1235) and work comes early in the morning

  29. anonymous
    • one year ago
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    Okay thank you. f(1)=2,f(n)=-3f(n-1)+[f(n-1)]^2

  30. amistre64
    • one year ago
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    well this ones just a exercise in plugging in the value ... show me your work for n=2

  31. amistre64
    • one year ago
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    dunno if it helps any to rewrite it by factoring: f(n) = f(n-1) [f(n-1) -3] your call

  32. anonymous
    • one year ago
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    Wait okay so do I plug 2 in for n?

  33. amistre64
    • one year ago
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    ideally yes, since 2 is the number after 1.

  34. anonymous
    • one year ago
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    Okay so I have f(2)=-3f(2-1)+[f(2-1)]^2

  35. amistre64
    • one year ago
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    good, and since 2-1 = 1 f(2) = -3 f(1) + [f(1)]^2 and what does f(1) equal?

  36. anonymous
    • one year ago
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    Im not sure in what to do after

  37. amistre64
    • one year ago
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    you replace f(1) with what its vale is, and work the math

  38. amistre64
    • one year ago
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    *value

  39. anonymous
    • one year ago
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    So would Imultiply -3 by 1? =-3

  40. anonymous
    • one year ago
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    Or where would I get the value from?

  41. amistre64
    • one year ago
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    f(1) has been defined for you already in your setup f(1)=2 <------ f(n)=-3f(n-1)+[f(n-1)]^2 ----------------- f(2) = -3 f(1) + [f(1)]^2 f(2) = -3(2) + 2^2 = -6+4 = -2 f(2) = -2 ------------------ we know f(2) now, so let n=3 and work the process again

  42. anonymous
    • one year ago
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    Okay thank you so much

  43. amistre64
    • one year ago
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    youre welcome .... once we know a new term, we can use it to find the next new term f(3) = -3 f(2) + [f(2)]^2 f(3) = -3(-2) + [-2]^2 = 6+4 f(3) = 10 ---------------- f(4) = -3 f(3) + [f(3)]^2 f(4) = -3(10) + 10^2 = 100-30 etc ....

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