Guest Posted February 10, 2009 Report Share Posted February 10, 2009 Find the next number. 2, 6.28, 61.98, 1921.77, 187197.87, ? I thought of this after reading the end of the riddle entitled "The End." posted by Riddle Master Zack Quote Link to post Share on other sites

0 Pickett 13 Posted February 10, 2009 Report Share Posted February 10, 2009 Well, finding the next number is really dependent on your rounding. it's almost easier just to give the formula used for the sequence: f(n) = 2pi^{(n(n-1)/2)} OR f(n) = f(n-1) * pi^{n-1}, where f(0) = 2 (rounded to 2 decimals) Specifically, what I did to get the numbers close to yours, is I used pi = 3.14159...so using the second formula I got the following: f(0) = 2 f(1) = f(0) * p^{0} = 2 f(2) = f(1) * pi^{1} = 2 * pi = 6.28 f(3) = f(2) * pi^{2} = 6.28 * pi^{2} = 61.98 f(4) = f(3) * pi^{3} = 61.98 * pi^{3} = 1921.77 f(5) = f(4) * pi^{4} = 1921.77 * pi^{4} = 187197.24 (this is probably just rounding "error") f(6) = f(5) * pi^{5} = 187197.24 * pi^{5} = 57285798.44 or, just using the first formula, it's close enough (again depending on rounding...and obviously these are slightly different) f(1) = 2pi^{(1(0)/2)} = 2pi^{0} = 2 f(2) = 2pi^{(2(1)/2)} = 2pi^{1} = 6.28 f(3) = 2pi^{(3(2)/2)} = 2pi^{3} = 62.01 f(4) = 2pi^{(4(3)/2)} = 2pi^{6} = 1922.77 f(5) = 2pi^{(5(4)/2)} = 2pi^{10} = 187294.51 f(6) = 2pi^{(6(5)/2)} = 2pi^{15} = 57315565.75 So, I would say the next number is about 57285798.44 or somewhere close to there... Quote Link to post Share on other sites

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Find the next number.

2, 6.28, 61.98, 1921.77, 187197.87, ?

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