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:   







 

RELATED QUESTIONS

the sequence 2, 3, 4, 6, 7, 8, 10, 11 consists of positive integers which are not perfect  (answered by richwmiller)

I need your help!! what is the nth term and 100th term in the sequence... (answered by stanbon,Timnewman)

I need to find the 100th term, for the sequence... (answered by Edwin McCravy)

I need to find the next number in a sequence but it is really challenging.
1, 11, 21,... (answered by rothauserc,ikleyn)

I need to know what number comes next in the following sequence 1 1 3 2 4 6 5... (answered by srinivas.g)

First question :

If P=2+4+6+8+...+104 and Q=6+8+10+12+...+106 are sums of arithmetic... (answered by ikleyn)

I want to know what number follows the sequence... (answered by Edwin McCravy)

Subject: locating a number in a triangular array of numbers 

[Question]
if the... (answered by scott8148)

	Identify the type of reasoning in the following situation:
You notice a pattern in the... (answered by edjones)