Tuesday 7 October 2014

Solve It

23:35    5 comments
Solve It If UR Genius



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5 comments:

  1. acubed29 March 2015 at 03:12

    A general solution is posted here . . . https://www.scribd.com/doc/260182194/Elementary-Sequences

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  2. Aladdin Bahian25 August 2016 at 10:46

    6

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  3. acubed28 October 2016 at 22:13

    It turns out the ‘?’ can be whatever we want it to be!

    Allow me to illustrate. Take for example, f(x)=(1/40)x^4-(13/20)x^3+(291/40)x^2-(553/20)x+42, and evaluate f(8), f(7), f(6), f(5), f(3). It turns out that:

    f(8)=56,
    f(7)=42,
    f(6)=30,
    f(5)=20,
    f(3)=9.

    Wait, what sorcery is this? Turns out that although the popular rule f(x)=x(x-1), which gives f(x)=6, satisfies the known values in the sequence, that f(x)=(1/40)x^4-(13/20)x^3+(291/40)x^2-(553/20)x+42 also satisfies them–except with a different value of f(3)!

    Here’s another one that also works but gives f(3)=12:
    f(x)=(1/20)x^4-(13/10)x^3+(271/20)x^2-(543/10)x+84

    And here is one where f(3)=π
    f(x)=(1/120)(π-6)x^4-(13/60)(π-6)x^3+(1/120)(251π-1386)x^2+(1/60)(3138-533π)x+14(π-6)

    Finally, in general if you want the ‘?’=k, i.e., f(3)=k where k is the value of your choice, then
    (1/120)(k-6)x^4-(13/60)(k-6)x^3+(1/120)(251k-1386)x^2+(1/60)(3138-533k)x+14(k-6)

    More details here: https://www.scribd.com/doc/260182194/Elementary-Sequences
    For a non-polynomial rule see here: http://i.imgur.com/BHkg0Ad.png

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  4. Vijay9 December 2018 at 20:56

    2

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  5. Unknown15 March 2019 at 19:33

    F(x) = x^2 - x
    F(3) = 6.
    Answer is 6.

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