we are in a college class called Mathematical Reasoning for Elementary Teachers class and i am stumped on this problem:
Find the missing terms in the following sequence:
2, 4, 8, 16, 30, _, _, _, 186, _

Question

we are in a college class called Mathematical Reasoning for Elementary Teachers class and i am stumped on this problem: 
Find the missing terms in the following sequence:
2, 4, 8, 16, 30, _, _, _, 186, _

dumbcow · Answer

i dunno, it doubles until 30...there is no way of knowing the exact pattern ??

anonymous · Answer

if you try to find a common difference you see that you need the 3rd difference, which means that your answer is in some form of an^3 + bn^2 + cn + d. From there you if you plug in values of n you can make a nice system of 4 equations. $$a(1)^3 + b(1)^2 + c(1) + d = 2 $$ $$a(2)^3 + b(2)^2 + c(2) + d =4$$ $$a(3)^3 + b(3)^2 + c(3) + d =8$$ $$a(4)^3 + b(4)^2 + c(4) + d = 16$$ 4 equations for 4 variables. If you solve it out you end with (8 n - 3 n^2 + n^3)/3 Then you just plug in for the remaining terms. This is a good problem, but not super useful for elementary teachers. Also if you want to cheat you can always http://www.wolframalpha.com/input/?i=2%2C+4%2C+8%2C+16%2C+30