Consider the sequence $3,9,\dots$

1. Assuming that the sequence is arithmetic with $t(1)$ as the first term, find the next four terms of the sequence and then write an equation for $t(n)$.

   Hint (a):

   Refer to the definitions of arithmetic and geometric sequences.

2. Assuming that the sequence is geometric with $t(1)$ as the first term, find the next four terms of the sequence and then write an equation for $t(n)$.

   Hint (b):

   Copy and complete the table below. What is the rule?

   $\left. \begin{array} { c | c } { n } & { 1 } \\ \hline t ( n ) & { 3 } & { 9 } & { 27 } \end{array} \right.$

3. Create a sequence that begins with $3$ that is neither arithmetic nor geometric. For your sequence, write the next four terms and, if you can, write a rule for $t(n)$.

   Hint (c):

   How can you make it neither arithmetic nor geometric?