Lets list the differences in the above list : these are 2 5 11 23 47:
call this list a
This last list has difference 3 6 12 24 (list b) so next number in this list is 48 and next number in list a is 47+48 = 95
In the original sequence therefore the next number is 89 + 95 = 184
so the list a and b are 2 5 11 23 47 95 List a
3 6 12 24 48 List b
The next number in list b is 96 and the next in list a is 96 + 95 = 191
so next number in sequence in question = 184 + 191 = 375
Next number in list b is 192 and next in list a = 191 + 192 = 383
So last number in sequence = 375 + 383 = 758
Next 3 numbers are 184, 383 and 758 answer
Sorry but I cant figure out the explicit rule at moment. I'll try and come back with it.