Question

5. The Fibonacci numbers fn are defined as follows: fi -1, f2-1, and f- fn-1+ f-2 for n 2 3, that is, from the third number on each number is the sum of the previous two numbers. The first ten Fibonacci numbers are: Find f11, f12, f13, and fia.

Answer 1

Answer with explanation:

The Fibonacci series is as follows:and it's first ten entries are

0,1,1,2,3,5,8,13,21,34,.....

You can see that after first two terms, each term that is from third term,sum of previous two consecutive terms.

1→1

2→0

3→1=1+0

4→2=1+1

5→3=2+1

6→5=3+2

7→8=5+3

8→13=5+8

9→21=13+8

10→34=21+13

$\rightarrow f_{11}=f_{10}+f_{9}\\\\=34+21\\\\f_{11}=55\\\\\rightarrow f_{12}=f_{11}+f_{10}\\\\=55+34\\\\f_{12}=89\\\\\rightarrow f_{13}=f_{12}+f_{11}\\\\=89+55\\\\f_{13}=144\\\\\rightarrow f_{ia}=f_{i(a-1)}+f_{i(a-2)}$