What is the pattern rule for this pattern 3-4-8-17-33?

Answer 1

After the initial number 3, the next number is generated by adding the square of numbers increasing by one at each step and starting with 12.

3 + 12 = 4

4 + 22 = 8

8 + 32 = 17

17 + 42 = 33....and so on

The series formula is U(n) = n3/3 - n2/2 + n/6 + 3, which can also be written as :-

3 + n/6(2n2 - 3n + 1) = 3 +n/6(2n - 1)(n - 1)