Given any number it is easy to find a rule based on a polynomial of order 6 such that the first six numbers are as listed in the question and the next is the given number. There are also non-polynomial solutions.
The simplest pule, using a polynomial of degree 5 is
T(n) = (43*n^5 - 740*n*4 + 4765*n^3 - 14140*n^2 + 19072*n - 8880)/120 for n = 1, 2, 3, ...
Accordingly, the next term is 101.
5.
4
4
Give me answer
21
1+1=2 1+2=3 2+3=5 ... 8+13=21
2
7
34
312 211 110 3-1=2 2-1=1 1-1=0
1 , 2, 4, 7, 11 +1,+2,+3,+4
The series goes like this 2 = 1^2 + 1^3 (1 square + 1 cube) 12 = 2^2 + 2^3 36 = 3^2 + 3^3 and so on.. So, the next number in the series is 6^2 + 6^3 = 252.