How would you invest $10,000 USD in the USA a week for 36 weeks. After that point the entire amount has to be returned. Meaning $360,000 I'm assuming treasury bonds but could you do a short term treasury bond?
Sure, you can buy treasury bills in $100 increments with terms of 4, 13, 26, and 52 weeks. You could also reinvest bills that are kept to maturity so that you get as much interest as possible. For example, you could buy a 26-week (6-month) bill with the first 10,000, then reinvest it with another 4-week bill at week 27, then reinvest that at week 31.
Note that technically you buy t-bills at a discount, so you might not be able to invest all $10,000 each week. Since you might spend, say, $9,910 for $10,000 in bills, you won't be able to invest every penny, but it shouldn't make a huge difference.
I also wouldn't expect much in terms of return for this. Since your average investment horizon is 18 weeks (.346 years), and the current t-bill rates for 13 and 26 week bills are 1.85% and 2.05%, you can expect an annualized return of about 1.95%, or about 0.6% for your investment, which would be about $2k.