11205
The number you're adding keeps getting multiplied by 7.
The sequence 1, 5, 33, 229, 1601 can be observed as each term being generated by a recursive formula. Specifically, each term can be expressed as ( a_n = 6a_{n-1} - 5a_{n-2} ), where ( a_0 = 1 ) and ( a_1 = 5 ). This pattern indicates that each term is a linear combination of the two preceding terms in the sequence.
what number comes next 1 -8 -16 -24 -33
229
33
143
11205 Pattern rule: Start at 1. Multiply by 7, and subtract 2.
The sequence 1, 5, 33, 229, 1601 can be observed as each term being generated by a recursive formula. Specifically, each term can be expressed as ( a_n = 6a_{n-1} - 5a_{n-2} ), where ( a_0 = 1 ) and ( a_1 = 5 ). This pattern indicates that each term is a linear combination of the two preceding terms in the sequence.
33
what number comes next 1 -8 -16 -24 -33
33
65
75
229
33
143
45
It is possible to find a polynomial of degree 5 such that it can be made to fit the pattern of the above five numbers and any number at all that is chosen to be the eighth. However, the simplest polynomial of degree 4 is Un = 36n4 - 336n3 + 1128n2 - 1568n + 741 for n = 1, 2, 3, ... and accordingly, the 8th term is 35,813.