0.1, 0.2, 0.4, 0.7, 1.2, 2.0, 2.13, 2.34, 2.68, 3.23, 4.12, 4.264, ...

Note: the original problem erroneously listed the last term of the sequence as 4.263 - this has been fixed

What was your method of coming up with these?  Armando, Egor, and Larry seem to disagree with you. 

This is what I had as my solution but in reading their posts I believe I made an error, and that they are indeed correct. This would make my last term 4.264, making the next terms 4.497, 4.874, and 5.484 as they have stated. 

I have lost my notes from when I submitted this problem.  The only way I could come up with to duplicate our sequence (last 4 terms of 4.263, 4.495, 4.87, and 5.477) was to accidentally use 143 (instead of 144) as the thirteenth Fibonacci term and then carry that forward in my calculations. Is it possible we made the same mistake or am I missing something.  I hate to ask a question about my own problem. 

The other thing I had figured that might have happened (and I do not want to question your integrity) was that you have access to the queue and just posted my submitted solution as the next three terms.  You are an apprentice though and unless you have another login do not have access to the queue. (again I apologize for questioning your integrity.)

I would like to post the solution but would like to get this cleared up first.  I will also petition Levik and indeed if the problem is in error, I will see if it can be corrected.