Chapter 14.2, Problem 71PE

A famous sequence in mathematics is called the Fibonacci sequence, named after the Italian mathematician Leonardo Fibonacci of the thirteenth century. The Fibonacci sequence is defined by

$\begin{array}{l}{a}_1=1\\ a_2=1\\ a_n=a_{n-1}+a_{n-2}\text{for}n>2\end{array}$

This definition implies that beginning with the third term, each term is the sum of the preceding two terms. Write out the first 10 terms of the Fibonacci sequence.