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))`