Your sequence will be a bunch of terms: and we can refer to each term by its index. The fifth term is . The th term is and so on.

If we pick some arbitrary term but want to indicate it might be any term we can call it be an arbitrary index. is the -th term. It could be the th term, or it could by the th term, . We don't know and don't care. We are refering to a non-specific term.

We are refering to a term when we don't know what position it is in. We say "let's call the position it is in: ".

Now, let's suppose I said "After picking that term look at the previous term" or "look at the next term". How can we refer to that. We if our term was the then the previous term would be .... . And if our term was the next term would be .... .

But how do we refer to it in general. If our term was what is the term immediately before it. Well, if this was the th term, the one write before it is the th term, .

So in this case:

means. "Pick any term. It is equal to the term before it plus two".

So if the previous term was equal to then this term, will be equal to .

So because we were told so.

And the previous term plus .

And and so on...

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