Question

Think of 3 rules, such that they generate 2,3,6 as the first 3 terms of a sequence.

Answer 1

1/2 3/2 -4

i came up with this one:\[\frac{1}{2}\left(\frac{n-1.5}{|n-1.5|}+\frac{3n-7.5}{|n-2.5|}-\frac{8n-280}{|n-3.5|}\right)\]

Answer 2

lol, i forgot to delete my reference scribbles

Answer 3

i was also considering coming up with something such that:\[\int_{0}^{n}f(x)dx=2,3,6~for~n=1,2,3\]

Answer 4

the first one i thought of was\[a_n=n^2-2n+3\]

Answer 5

hmm; such that the first area is 2, and the second is 1, and the third is 3