Found 8 solutions by oscargut, solver91311, tinbar, nyc_function, gurungsantosh, MathTherapy, acubed1234, mbessearch:Answer by oscargut(2103) (Show Source): You can put this solution on YOUR website! 3x2 = 6
I can help you with more questions at: mthman@gmail.com
Thanks
Answer by acubed1234(5) (Show Source): You can put this solution on YOUR website! 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
Answer by mbessearch(2) (Show Source): You can put this solution on YOUR website! The answer is 3. Equal means equals. While the various functions and formulas displayed elsewhere in answer would be reasonable if shown, without them, there are four wrong answers. One of the beauties of Math is that it is precise. Do not use equals unless you mean equals.
