If I conceived September 1st, my doctor told me there would be no sign of a sac yet @ 4 weeks.
That's still an average size for how far along you would be with a conception date of Aug 31st. However, sperm can live in the body from 3-5 days, so if sex on the 17th was after your period finished, it could have essentially lived in your cervix and fertilized the egg within those 3-5 days. So, for example, you had sex on cd 5, but ovulated on cd 9 - you still could have very easily gotten pregnant.
Sorry! I had my dates mixed up. I hsd sex Aug 17 and my period around tAug 12th. My gestational sac wouldn't be as big if it was Aug 31. Its 14 mm.
If your last period was on the 12, you probably got pregnant from intercourse on the 31st of August. Pregnancy dates start at the first day of your last cycle, so that would technically put you at 7 weeks as of 9/30 (this coming Monday).
You could have... I have heard of women getting pregnant on their period, but you should probably ask your doctor. Usually they tell you the closest date of conception.