Answer
a) $4,7,12,19,28,39,52,67,84,103$
b) see graph
c) $415$
Work Step by Step
a) In order to find the first ten terms of the given sequence $a_n=3+n^2$ put the graphing calculator in $\textit{sequence}$ mode and $\textit{dot}$ mode, enter the sequence ($3+n^2$), then use the $\textit{table}$ feature to see the terms of the sequence. The first ten terms are:
$$\begin{align*}
a_1&=4\\
a_2&=7\\
a_3&=12\\
a_4&=19\\
a_5&=28\\
a_6&=39\\
a_7&=52\\
a_8&=67\\
a_9&=84\\
a_{10}&=103.
\end{align*}$$
b) We set the viewing window so that $0\leq n\leq 10$, $0\leq x\leq 11$ and $0\leq y\leq 110$. Graph the sequence and use the $\textit{trace}$ feature to view the terms.
c) With the $\textit{summation}$ feature we find the sum of the first ten terms of the sequence:
$$sum(seq(3+n^2,n,1,10))=415.$$
