# Seatwork (Sequences and Summations)

Write down the first $10$ terms, ($n=0,1,2,\cdots,9$) of the following sequences
1.
$$
a_n=3+4n
$$

2.
$$
a_n=5(4^n)
$$

3.
$$
\begin{align*}
a_0&=2\\
a_1&=1\\
a_n&=a_{n-1}+a_{n-1}
\end{align*}
$$

Solve the closed form formula for the following recurrence relations

1. $$
\begin{align*}
a_0&=5\\
a_n&=a_{n-1}+4
\end{align*}
$$

2. $$
\begin{align*}
a_0&=1\\
a_n&=3a_{n-1}+2
\end{align*}
$$

3. $$
\begin{align*}
a_0&=2\\
a_n&=4a_{n-1}-1
\end{align*}
$$

Solve for the following sums

1. $$
\sum_{i=3}^{8}{a_i}\\
\text{where } \{a_i\} \text{ is the sequence of the terms: }a_n=5(3^n)
$$

2.
$$
\sum_{i=0}^{10}{\sum_{j=0}^{i}{8j}}
$$