College Algebra, Chapter 9, 9.1, Section 9.1, Problem 24

a.) Determine the first 10 terms of the sequence given by $a_n = a_{n- 1} - a_{n-2}$ that is defined recursively by $a = 1$ and $a_2 = 3$

$
\begin{equation}
\begin{aligned}
a_1 &= 1\\
\\
a_2 &= 3\\
\\
a_3 &= a_2- a_1 = 3-1 = 2\\
\\
a_4 &= a_3- a_2 = 2-3 = -1\\
\\
a_5 &= a_4- a_3 = -3-(-1) = -3\\
\\
a_6 &= a_5- a_4 = -2-(-3) = -2\\
\\
a_7 &= a_6- a_5 = -2-(-3) = 1\\
\\
a_8 &= a_7- a_6 = 1 - (-2) = 3\\
\\
a_9 &= a_8- a_7 = 3 - 1 = 2\\
\\
a_{10}&= a_9- a_8 = 2-3 = -1
\end{aligned}
\end{equation}
$

b.) Graph the first 10 terms of the sequence