27-Apr-2012, 12:06 PM
Quote:an<sup>3</sup> + bn<sup>2</sup> + cn + d = f(n) for all n
a + b + c + d = 1
8a + 4b + 2c + d = 4
27a + 9b + 3c + d = 10
64a + 16b + 4c + d = 20
...so the coefficients are always the same; only the numbers at the end change? And so I assume that if you had five numbers in the sequence, you would include a variable "e" and include exponents of 5 in the last equation?
Crazy stuff. This thread is proving to be very educational.
Quote:In Jr. High School, I would take a gummi bear, squeeze its ears into points so it looked like Yoda, and then I would say to it "Eat you, I will!". And of course then I would it eat.