Well, the sequence of 9 times each term is

9,99,999,9999,...

And each term of that is one less than each term of this sequence

10,100,1000,10000...

which is the sequence with nth term 

So the sequence 9,99,999,9999,... has nth term 

And each term of the desired sequence 1,11,111,1111,... 
is th of the coresponding term of that,

So the desired sequence is 
 
It is both a pattern, progression and a sequence.

Are all sequences patterns or it is the other way.

Similarly are all sequences progressions or it is the other way.

It's the other way around, all progressions are sequences.

But not all sequences are progressions begause not all sequences 
get larger and larger(i.e., progress).

Edwin