[Guest]

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

[Pickett]

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) * p⁰ = 2

f(2) = f(1) * pi¹ = 2 * pi = 6.28

f(3) = f(2) * pi² = 6.28 * pi² = 61.98

f(4) = f(3) * pi³ = 61.98 * pi³ = 1921.77

f(5) = f(4) * pi⁴ = 1921.77 * pi⁴ = 187197.24 (this is probably just rounding "error")

f(6) = f(5) * pi⁵ = 187197.24 * pi⁵ = 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) = 2pi⁰ = 2

f(2) = 2pi^(2(1)/2) = 2pi¹ = 6.28

f(3) = 2pi^(3(2)/2) = 2pi³ = 62.01

f(4) = 2pi^(4(3)/2) = 2pi⁶ = 1922.77

f(5) = 2pi^(5(4)/2) = 2pi¹⁰ = 187294.51

f(6) = 2pi^(6(5)/2) = 2pi¹⁵ = 57315565.75

So, I would say the next number is about 57285798.44 or somewhere close to there...