It is very usual that major search engines cache pages and show the link as "cached". Now if I make changes to my website, it takes nearly a week to get cached. In the meantime will the SE consider my current page for SERPs or the cached page?
As said, the title in the SERPs is what Google has cached.
If you want to influence how long Google keeps your web pages cached, you can use a "noarchive" meta tag to tell Google not to cache your page and/or use an "expires" meta tag to tell Google to keep your web page cached for a short time only.
Note that both of these methods are not full-proof. Google still makes up its own mind about what to show.