Today we continued working with geometric sequences and recursive definitions. The first slide shows an application of a geometric sequence to a real world problem. The trick is to turn the word problem into a simple geometric sequence problem. Finding n was trickier than expected and was the key to the problem. Once we made a table then it was pretty obvious that n = 11.
The rest of class was spent making recursive definitions. One problem missing from the slides was finding the recursive formula for the Fibonacci sequence. One formula could be
t(1) = 1, t(2) = 1, and t(n) = t(n-1) + t(n-2), for n > 2.
Another way to write the Fibonacci function is:
F(0) = 0, F(1) = 1, F(n) = F(n-1) + F(n-2), for n > 1
The last slide shows a problem to try at home.
Make the table!
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