SOLUTION: how do you find the recursive formula of the sequence 1,1,2,3,5,8...?
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Question 585639: how do you find the recursive formula of the sequence 1,1,2,3,5,8...?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
This is the fibonacci sequence. The first two terms are given as 1,1
The third term is then the sum of the previous two terms: 1+1 = 2
The fourth term is then the sum of the previous two terms: 1+2 = 3
The fifth term is then the sum of the previous two terms: 2+3 = 5
The sixth term is then the sum of the previous two terms: 3+5 = 8
and so on...
So the recursive formula is
 = \begin{cases} 1 & \text{if } n = 0 \\ 1 & \text{if } n = 1 \\ f(n-1) + f(n-2) & \text{if } n \ge 2 \\ \end{cases} "\large f(n) = \begin{cases} 1 & \text{if } n = 0 \\ 1 & \text{if } n = 1 \\ f(n-1) + f(n-2) & \text{if } n \ge 2 \\ \end{cases}")
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