Question 199930
I want to know the difference between a sequence and a progression.

A progression is a sequence in which the terms get successively larger. 


 Are these two different from a pattern? Can you cite some examples. Is 1,11,111,1111,... a sequence or a pattern. 
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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 {{{a[n]=10^n}}}

So the sequence 9,99,999,9999,... has nth term {{{a[n]=10^n-1}}}

And each term of the desired sequence 1,11,111,1111,... 
is {{{1/9}}}th of the coresponding term of that,

So the desired sequence is {{{a[n]=(10^n-1)/9}}}
 
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</pre>