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Math Help - Basic Sequence

  1. #1
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    Basic Sequence

    if
    tn+1=2tn+tn-1

    t1=1
    t2=3

    What's the next 3 numbers of the sequence?

    I don't understand the question - anyone help?
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  2. #2
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    7, 17, 41
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  3. #3
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    yea - but i don't understand why - anyone explain?
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  4. #4
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    t_(n + 1) = 2t_n + t_(n - 1) is equivalent to t_n = 2t_(n - 1) + t_(n - 2).
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  5. #5
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    For example, let n = 3. t_3 = 2t_(3 - 1) + t_(3 - 2) = 2t_2 + t_1 = 2 3 + 1 = 7. Repeat for n = 4 and 5.
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  6. #6
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    Oh ok - I kind of get it
    But Johnny - you said :

    t_(n + 1) = 2t_n + t_(n - 1) is equivalent to t_n = 2t_(n - 1) + t_(n - 2).

    How did you get from the first equation to the second?
    Is there an algebraic operation that i can do ?
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  7. #7
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    t_(n + 1) = 2t_n + t_(n - 1) is read as third number is equal to 2 times second number plus first number, hence n, n - 1 and n - 2 is logically the same thing.
    Also, I did this because it's easier to calculate the third number.
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  8. #8
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    So no algebra steps whatsoever?
    ..
    ok then
    Thanks anyways
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  9. #9
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    Hello, qwertyuiop!

    If t(n+1) = 2t(n) + t(n-1) . and t(1) = 1, t(2) = 3,

    what are the next 3 numbers of the sequence?

    It seems that you don't understand that the equation says:

    . . "A term is equal to twice the preceding term, plus the term before that."


    We have: .t(1) = 1

    . . . . . . . .t(2) = 3

    Then: .t(3) .= .2(3) + 1 .= .7

    Then: .t(4) .= .2(7) + 3 .= .17

    Then: .t(5) .= .2(17) + 7 .= .41


    Get it?

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  10. #10
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    ohh i see i see
    Thanks !
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