Question 1144231

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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 {{{ highlight( 599 ) }}}


Another way to go is to recognize that the sequence is
{{{ a[n] = 6n - 1 }}} for n = 1,2,3, ...

and plug in 100:   {{{ a[100] = 6*100 - 1 = 599 }}}