3,8,17,32,57, () mathematical reasoning

3,8,17,32,57, () mathematical reasoning

Fill in 98
First calculate the difference between the two, they are 5,9,15,25.. there is a rule between them, that is, the first two values are added, and then 1 is the value of this term, for example, 5 + 9 + 1 = 15; 9 + 15 + 1 = 25; then 15 + 25 + 1 = 41, so now the number is 57 + 41 = 98

Multistage sequence 3,8,17,32,57, ()
It's like this. There's a math problem in the book, which is multi-level sequence. 8,17,32,57, ()
I used the method in the book to make the difference three times, that is, subtracting the former from the latter. The first difference is 5,9,15,25, ()
The second time is 4,6,10, (). The third time is 2,4, (). How to guess that it is an equal ratio sequence in the book, and 4 should be followed by 8. But why is it not an equal difference sequence, or 2,4,6!

3=1^2+2^1
8=2^2+2^2
17=3^2+2^3
32=4^2+2^4
57=5^2+2^5
The rule is n ^ 2 + 2 ^ n
The next item should be 6 ^ 2 + 2 ^ 6 = 100

Finding sequence 2,8,17,31,52
2, 8, 17, 31, 52 what's next

82. This is a second-order arithmetic sequence problem: the difference between the last digit and the first digit is 6,9,14,21 respectively. The difference between the last digit and the first digit of this sequence is 3,5,7,9 respectively. So 21 + 9 = 30,52 + 30 = 82

Sequence 5,9,17,23, X X in is equal to
A47 B65 C63 D128

Option B 65
5=2^2+1
9=2^3+1
17=2^4+1
33=2^5+1
65=2^6+1
Your item 4 should be 33 instead of 23. It's wrong in the book