More importantly this silly question is one which I can't answer. First some history though, as to why I will be posting an A Level maths question in two ticks.
Before I went on holiday, a friend of mine from school/college bumped into me in town. We enquired as to how the other was, and then I was asked whether I would consider helping someone with their AS level maths. I was reluctant and said that I will think about it, so we just exchanged details and left it at that. However the day before I left for my holiday, I had a voice mail message asking the same question. So I replied by asking my friend to get in touch with me after I returned (in case they found someone else).
Upon my return a prompt email found itself in my inbox, and so began my journey of helping my friends niece with her AS Maths. Her mother was willing to pay £15 an hour, but I thought that since this was my first time doing such a thing, and it was a favour, £12.50 would be reasonable. So she started coming to my house on Saturday and Sunday for an hour and I helped her with her maths. On her first visit we drew up a list of topics which included trigonometry, sequences and series, the binomial expansion, etc.
I didn't really know what was expected of me in this role, but I soon realised that it was no easy job. Today was the last time she came because her exams on Monday, but boy has it been difficult. I would say that her lack of enthusiasm for maths was her biggest barrier, coupled with the fact that she very easily lost her confidence and motivation.
I had to swot up on A level maths again, and not all of it was easy. I hate trigonometry, namely the CAST diagrams and I also didn't like sequences (which the question below happens to be about!) The job required a lot of patience indeed, however I think I enjoyed it. Well I enjoyed it enough to do it again. I can't really write much else about what I have learnt by doing this (etc) since I have a massive, crunching headache and I'm typing with one hand! However, if I was to do it again the price will definitely change-- I have since been told that £12.50 was a complete and utter bargain! (Quite a lot of people are charging £22 per hour for A level tuition...) I think £18 an hour seems reasonable, but hey, I don't think I will ever do this again. It was just a favour (which gave me some money to buy the maths books from the Springer sale--woohoo!)
So the question (without a calculator by the way!) which is really bugging me is:
A sequence is defined by the recursion relation,
Given a=20 and u_1=3 find u_2, u_3 and u_4. Giving your answers to 2 decimal places.
We have an expression for u_2 but how the heck are you meant to give it to 2dp? I have missed something vital and it will hit me soon, but not soon enough. So if anyone has any ideas, please put me out of my misery!
I think I really enjoy teaching, but it is damn hard work. Preparing lessons, finding good questions, marking work and you have to be on the ball yourself otherwise you get "the look", which I am famous for giving myself! (I think, having been somewhat a difficult student myself (in the sense that I can be really dumb at times) I tried to cover all hurdles etc that I faced.) It is the challenging aspect of it which I find appealing.