Find the next number in the following series:

11, 12, 20, 23, 33, 46, ?, ?

Although I like the
fibo solution I would like to emphasize the point that no series can be uniquely defined by presenting a number (huge as it may) of its members.

1, 2, 3 , 4 ,5 ... does not imply a(n)=n and the next member is not necessarily 6...!!
It could be inter alia 126 if a(n)=(n-1)*( n-2)*( n-3)*( n-4)*( n-5) +n

re :our series
I am free to assume a polynomial formula (5th degree since 6 numbers were given/ two numbers would give a linear form, 3 -quadratic etc).

a(n)= A*N^5+B*N^4+C*N^3+D*N^2+H*N+F
WE GET:
A+B+C+D+H+F=11
32*A+16*B+8*C+4*D+2*H+F=12
243*A+81*B+27*C+9*D+3*H+F=20
1024*A+256*B+64*C+16*D+4*H+F=23
3125*A+625*B+125*C+25*D+5*H+F=33
7776*A+1296*B+216*C+36*D+6*H+F=46

SOLVE

A=-1/3
B=6
C=-121/3
D=251/2
H=-1037/6
F=93
AND a(7)= 2 a(8)=-255

AS GOOD AS ANY OTHER
ADY

Posted by Ady TZIDON on 2004-02-18 11:27:55