It is possible to find a polynomial of order 6 that will generate the above sequence of numbers and ANY seventh number. And, there are non-polynomial rules that will do the same.
The simplest polynomial is
Un = (177n5 - 3030n4 + 19475n3 - 57990n2 + 78688n - 27600)/120 for n = 1, 2, 3, ... and, according to this rule, the next number is 512.
81
-243
The next number is 243, because 81x3=243.
651 is the next number.
20
243
625
81
-243
The next number is 20.
It is '3' to the power(exponent) of 'n-1'. #1 ; 3^(1-1) = 3^(0) = 1 #2 ; 3^(2 -1) = 3^(1) = 3 #3 ; 3^(3-1) = 3^(2) = 9 #4 ; 3^(4-1) = 3^(3) = 27 #5 ; 3^(5-1) = 3^(4) = 81 #6 ; 3^(6-1) = 3^(5) = 243 #n th term ; 3^(n - 1) et seq.,
The next number is 243, because 81x3=243.
651 is the next number.
225
81
45 54
20