Chapter 8, Problem 2CA

To determine

To find: It is being asked to find all the numbers between 0 and 100 that are in the range of the function defined here.

Answer to Problem 2CA

The numbers are 1,2,3,5,8,13,21,34,55,89.

Explanation of Solution

Given information: The given values of the function and rule are

  $\begin{array}{l}f(1)=1\\ f(2)=1\\ f(n)=f(n-1)+f(n-2)\end{array}$

Let’s find the value of $f(3),f(4),f(5),\mathrm{...}$ till it reaches 100 or less

  $f(3)=f(3-1)+f(3-2)$

  $=f(2)+f(1)$

Plug in the values of $f(1)$ and $f(2)$ .

  $=1+1=2$

Now, let’s find all the terms,

  $f(4)=f(3)+f(2)=2+1=3$

  $f(5)=f(4)+f(3)=3+2=5$

  $f(6)=f(5)+f(4)=5+3=8$

  $f(7)=f(6)+f(5)=8+5=13$

  $f(8)=f(7)+f(6)=13+8=21$

  $f(9)=f(8)+f(7)=21+13=34$

  $f(10)=f(9)+f(8)=34+21=55$

  $f(11)=f(10)+f(9)=55+34=89$

Here $f(12)$ would exceed 100.

The numbers are 1,2,3,5,8,13,21,34,55,89.