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    I found the formula for the sum for this sequence and it turns out to be

    S_n =F_{n+2} -1


    So i tried to add the 2 numbers you see there and get 288 and take 1 you get 287 but of course this isn't the right number

    so i decided to find the general solution which happened to be

    a_n =\dfrac{1}{\sqrt 5} \cdot  \left(\dfrac{1+\sqrt 5}{2} \right)^n - \dfrac{1}{\sqrt 5} \cdot \left(\dfrac{1-\sqrt 5}{2} \right)^n

    and the 12th term happens to be 377 and i took 1 off of this and it's still wrong, i don't get where i'm going wrong.
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    (Original post by will'o'wisp2)
    https://cdn.discordapp.com/attachmen...63/unknown.png

    I found the formula for the sum for this sequence and it turns out to be

    S_n =F_{n+2} -1


    So i tried to add the 2 numbers you see there and get 288 and take 1 you get 287 but of course this isn't the right number

    so i decided to find the general solution which happened to be

    a_n =\dfrac{1}{\sqrt 5} \cdot  \left(\dfrac{1+\sqrt 5}{2} \right)^n - \dfrac{1}{\sqrt 5} \cdot \left(\dfrac{1-\sqrt 5}{2} \right)^n

    and the 12th term happens to be 377 and i took 1 off of this and it's still wrong, i don't get where i'm going wrong.
    S_{12}=F_{14}-1 so you need n=14 in the Fibonacci number formula.

    Why do they say that F_{12}=F_{13}=144...? That's not right.

    F_{12}=144 and F_{13}=233

    Did you derive the correct relation for S_n?
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    It's possible there's some confusion between "nth term" and a_n, given they start the series with a_0.

    That said, under their definitions we get the sum

    1+1+2+3+5+8+13+21+34+55+89+144=3 76

    I can't really see how that's debatable (i.e. if there is confusion, it's them who are confused...)
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    Your expression for S_n is correct and your answer is definitely correct, if the value for F_{13} was indeed a typo. I'm not sure how you could possible get F_{12} = F_{13} = 144 on the off-chance it's not a typo though...
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    (Original post by RDKGames)
    S_{12}=F_{14}-1 so you need n=14 in the Fibonacci number formula.

    Why do they say that F_{12}=F_{13}=144...? That's not right.

    F_{12}=144 and F_{13}=233

    Did you derive the correct relation for S_n?
    sorry i meant that the 14th term is actually 377 my bad. The 12th term si actually 144 tho but the 13th term certainly isn't 144 i was confused by that too which is why i got the general solution.

    But i have no idea how to derive that , hence i used this "trusty" site and found it out.
    https://www.quora.com/What-is-the-su...bonacci-series
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    Couple of notes: you're not "supposed" to just add it up, but note that it only really takes a few seconds to do this by hand. Worth remembering when you need to do this in an exam.

    Similarly, the formula you give is probably more hassle than it's worth until about the 377 term.

    Finally, for n > 2 (or so), you can ignore the 2nd term in the formula and instead just pick the closest integer to the 1st term. Saves time + effort.
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    (Original post by DFranklin)
    It's possible there's some confusion between "nth term" and a_n, given they start the series with a_0.

    That said, under their definitions we get the sum

    1+1+2+3+5+8+13+21+34+55+89+144=3 76

    I can't really see how that's debatable (i.e. if there is confusion, it's them who are confused...)
    HOLY MOLEY I WAS RIGHT? What is this, a miracle?
    (Original post by _gcx)
    Your expression for S_n is correct and your answer is definitely correct, if the value for F_{13} was indeed a typo. I'm not sure how you could possible get F_{12} = F_{13} = 144 on the off-chance it's not a typo though...
    HAHA LOL YOU THOUGHT IT WAS A TYPO? LOOK AGAIN

    (btw i had to refresh the page so different numbers came up)
    https://cdn.discordapp.com/attachmen...00/unknown.png
    (Original post by DFranklin)
    Couple of notes: you're not "supposed" to just add it up, but note that it only really takes a few seconds to do this by hand. Worth remembering when you need to do this in an exam.

    Similarly, the formula you give is probably more hassle than it's worth until about the 377 term.

    Finally, for n > 2 (or so), you can ignore the 2nd term in the formula and instead just pick the closest integer to the 1st term. Saves time + effort.
    not quite sure i understand this
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    (Original post by will'o'wisp2)
    HOLY MOLEY I WAS RIGHT? What is this, a miracle?

    HAHA LOL YOU THOUGHT IT WAS A TYPO? LOOK AGAIN

    (btw i had to refresh the page so different numbers came up)
    https://cdn.discordapp.com/attachmen...00/unknown.png


    not quite sure i understand this
    The only way that could possibly make sense would be if F_{n} = F_{n-1} + F_{n-2} except when n=24, where F_{24} = 28,657, which would be pretty weird.
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    (Original post by will'o'wisp2)
    not quite sure i understand this
    e.g.

    n = 10, \dfrac{1}{\sqrt{5}} \left(\dfrac{1+\sqrt{5}}{2} \right)^n = 55.0036361...; nearest integer is 55.

    n = 20, \dfrac{1}{\sqrt{5}} \left(\dfrac{1+\sqrt{5}}{2} \right)^n = 6,765.0000296...; nearest integer is 6765
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    (Original post by DFranklin)
    e.g.

    n = 10, \dfrac{1}{\sqrt{5}} \left(\dfrac{1+\sqrt{5}}{2} \right)^n = 55.0036361...; nearest integer is 55.

    n = 20, \dfrac{1}{\sqrt{5}} \left(\dfrac{1+\sqrt{5}}{2} \right)^n = 6,765.0000296...; nearest integer is 6765
    Oh so it gives quite a good accurate approximation
 
 
 
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