Consider the sequence $3, 9, …$

1. Assuming that the sequence is arithmetic, what are the next four terms of the sequence? Write an equation for $t\left(n\right)$.

   Hint (a):

   Remember that in an arithmetic sequence each term is equal to the one before plus some number.

2. Assuming that the sequence is geometric, what are the next four terms of the sequence? Write an equation for $t\left(n\right)$.

   Hint (b):

   Notice that the first term is the base raised to the first power, and the second to the second power.

   Answer (b):

   $27, 81, 243, 729$

   $t\left(n\right) = 3^{n}$

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 an equation for $t\left(n\right)$.

   Hint (c):

   Think of sequences with both addition and subtraction, or any other combination of operations.