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anonymous

  • one year ago

1 Question Algebra 2

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  1. anonymous
    • one year ago
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  2. UsukiDoll
    • one year ago
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    Recursion is the process of choosing a starting term and repeatedly applying the same process to each term to arrive at the following term. Recursion requires that you know the value of the term immediately before the term you are trying to find.

  3. Jack1
    • one year ago
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    yay, cheers @KimberlyAlice and @UsukiDoll ;P

  4. anonymous
    • one year ago
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    Okay, so how would I find the equation for this problem? Thanks @Jack1 :P

  5. UsukiDoll
    • one year ago
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    so examples of recursion formulas are \[a_1 = 4, a_n = 2a_{n-1}\] or \[a_1=4 , a_{n+1} = 2a_n\]

  6. UsukiDoll
    • one year ago
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    so what is the \[a_1 \] in this problem?

  7. UsukiDoll
    • one year ago
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    we need to know what a_1 is or we are stuck

  8. anonymous
    • one year ago
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    a1 would be the recursive number?

  9. UsukiDoll
    • one year ago
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    well we need to figure out the next term it's like a chain.. but we need it to start at \[a_n \] where n = 1

  10. UsukiDoll
    • one year ago
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    what's the starting number? that's a_n when n =1

  11. anonymous
    • one year ago
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    7

  12. UsukiDoll
    • one year ago
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    ok.. so \[\large a_1=7\]

  13. anonymous
    • one year ago
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    That limits the choices to B and D

  14. UsukiDoll
    • one year ago
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    so now we need to figure out ... we need to get to 4 somehow but what recursion formula will allow us to do that

  15. anonymous
    • one year ago
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    B

  16. anonymous
    • one year ago
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    No wait...we would get 3

  17. UsukiDoll
    • one year ago
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    yeah that's what I mean.. we need to get to 4's land

  18. UsukiDoll
    • one year ago
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    we know the difference in each number is 3

  19. anonymous
    • one year ago
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    Yes

  20. anonymous
    • one year ago
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    So it would be B?

  21. UsukiDoll
    • one year ago
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    let me think...

  22. UsukiDoll
    • one year ago
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    alright our starting point is \[a_1 = 7 \] so now we need a formula to get to 4

  23. UsukiDoll
    • one year ago
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    OH how I wish I can do this \[a_n=a_{n-1}-3 \] where n = 2 \[a_2=a_{2-1}-3 \] \[a_2=a_{1}-3 \] since \[a_1 = 7\] \[a_2=7-3 \] \[a_2=4 \]

  24. UsukiDoll
    • one year ago
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    ok I think the multiple choices are flawed. Just look what I've done.. I got a_2 to appear as 4

  25. UsukiDoll
    • one year ago
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    hey! There's a typo in your choices. You want the last choice with a - sign instead

  26. anonymous
    • one year ago
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    oh no...

  27. UsukiDoll
    • one year ago
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    And I'll prove it so now we have \[a_1 = 7, a_2 =4\] so now our next recursive formula \[a_n=a_{n-1}-3 \] let n = 3 \[a_3=a_{3-1}-3\] \[a_3=a_{2}-3\] since \[a_2=4 \] \[a_3=4-3\] \[a_3=1\]

  28. UsukiDoll
    • one year ago
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    see the pattern ... Now I have 7 4 1

  29. UsukiDoll
    • one year ago
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    so I have to do this 3 more times... for -2 -5 and ?!

  30. anonymous
    • one year ago
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    I'm confused...which answer choice is this?

  31. UsukiDoll
    • one year ago
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    or maybe not.. \[a_4 = -2, a_5 = -5\]

  32. UsukiDoll
    • one year ago
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    there's a typo in the choice we need

  33. anonymous
    • one year ago
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    But it would be D?

  34. UsukiDoll
    • one year ago
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    but.. .we can use the formula I have to get our next number.. we know that a_1 = 7 we need a_6

  35. UsukiDoll
    • one year ago
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    \[{a_6}=a_{6-1}-3\] \[{a_6}=a_{5}-3\] since \[a_5= -5\] \[{a_6}=-5-3\] \[{a_6}=-8\]

  36. UsukiDoll
    • one year ago
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    It's the last choice with that typo that shouldn't be there.!!!!

  37. UsukiDoll
    • one year ago
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    because should that stand... a_1 would've been 10 if it was subtraction it would've been 4

  38. Jack1
    • one year ago
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    why not \(\Large a_n = 10 -3(n)\)?

  39. Jack1
    • one year ago
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    @UsukiDoll doesnt that fit?

  40. UsukiDoll
    • one year ago
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    look at the choices we are given

  41. Jack1
    • one year ago
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    ah, my bad, sorry :/

  42. UsukiDoll
    • one year ago
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    it's the last choice with the typo. trust me! We got the beginning which is a_1 is 7 we needed to find a_6 which is -8

  43. anonymous
    • one year ago
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    Thank you for all your help @Jack1 and @UsukiDoll

  44. Jack1
    • one year ago
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    np but psh, was all @UsukiDoll , i did nothing

  45. UsukiDoll
    • one year ago
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    "because should that stand... a_1 would've been 10 if it was subtraction it would've been 4 " oy I meant a_2 would've been 10 if we had a + a_1 = 7 a_2 =4 a_3 =1 a_4 =-2 a_5 = -5 a_6 = -8 but the formula is \[\large a_n=a_{n-1}-3 \]

  46. anonymous
    • one year ago
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    I understand. thank you!

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