One way to solve this is to operate on the original sequence so it is in correspondence to 1,2,3,..., 100 then reverse the steps:
I. 5, 11, 17, 23, ...
If you subtract 5 from each element:
II. 0, 6, 12, 18, ...
Then divide each element by 6:
III. 0, 1, 2, 3, ...
Then add 1 to each element:
IV. 1, 2, 3, 4, ...
We can now work our way back from IV to I, reversing the operations:
The 100th element in IV will be 100 (simple counting from 1 to 100)
The 100th element in III will be 99 (subtracted 1)
The 100th element in II will be 594 (multiplied by 6)
The 100th element in I will be 599 (added 5)
The 100th element of the sequence is 
Another way to go is to recognize that the sequence is
for n = 1,2,3, ...
and plug in 100: 
