Question: I'd like to know whether "the survey online" or "an online survey" should be used in the following:

> 
> World Gym has been under new management since July 3. For the new team to better serve our members, please take a few moments and click here to fill out **the survey online / an online survey**.
> 
> 
> 

I'd appreciate your help.

Answer: 
The chosen article reveals the speaker's thought.

With **the** the speaker is indicating that he or she believes you will understand (you, being the visitor reading those words) that **a survey** is normally associated with attempts to get to know users better, and **the particular survey in this instance** can be reached by clicking the link.

That thought might not even be fully conscious on the speaker's part.

This "previously mentioned" rule must be understood very very very very very broadly, so that it would include under its aegis what is typical or usual under the circumstances. It is a previous *encounter* not necessarily a previous *mention*, and the encounter need not have taken place in the immediate speech context. The immediate speech context can allude to a general context where the encounter has occurred or is believed by the speaker to have occurred.
The survey is **very specific here.** How? Because it says *click here.* Anything specific i.e. *only that thing and nothing else* would have the definite article. Take another example and you may understand that -

> 
> If you want to register, click here to go to **the registration form.**
> 
> 
> 

So, registration here is specific for that login, for that page. 

Had it been an indefinite article, I would think of some other *form or feedback* which could be related to the website *but* not specific to the matter you are talking about. 

Finally, ask yourself, is that the **only survey** for that activity? If yes, then go for the definite article.