I'm not sure if I understood ya, but I read it as you'll get the first oil change w/ synthetic & then doing oil changes at 3k, but not using synthetic for it.
If I understand that correctly, I'd say ya actually don't need to change your oil every 3k using synthetic.
For that matter, you don't need to change oil every 3k using regular oil either. There's been articles in various publications stating this very thing & my mechanic confirmed it. Todays vehicles can go a lot longer between oil changes.
You will need to add oil during that time, but you won't need to change it.
Here's a link about the oil change intervals. If you want more just google "Oil Change Intervals" & you'll get a lot of articles similar to this one.
http://skepticblog.org/2009/02/22/oilchange-rant/
So with even regular oils/modern engines allowing for more time between intervals & I use synthetic on top of it, I tend to go 8-10,000 miles between oil changes. There's even a Mobile 1 synthetic that advertises you can go 15K between changes. That might be pushing it, but it's what they advertise.
Again, you will need to add oil during this time. Ya just don't have to change it as often.
you might crack a few ribs from the rough ride take it down a little
