---
# System prepended metadata

title: Seatwork (Sequences and Summations)

---

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


