A sequence starts with the terms 1 and 10.

1. Find the next two terms if it is arithmetic: 1, 10, \(\underline{\hspace{.25in}}\), \(\underline{\hspace{.25in}}\).
2. Find the next two terms if it is geometric: 1, 10, \(\underline{\hspace{.25in}}\), \(\underline{\hspace{.25in}}\).
3. Find two possible next terms if it is neither arithmetic nor geometric: 1, 10, \(\underline{\hspace{.25in}}\), \(\underline{\hspace{.25in}}\).

Complete each geometric sequence with the missing terms. Then find the growth factor for each.

1. \(\underline{\hspace{.25in}}\), 5, 25, \(\underline{\hspace{.25in}}\), 625
2. -1, \(\underline{\hspace{.25in}}\), -36, 216, \(\underline{\hspace{.25in}}\)
3. 10, 5, \(\underline{\hspace{.25in}}\), \(\underline{\hspace{.25in}}\), 0.625
4. \(\underline{\hspace{.25in}}\), \(\underline{\hspace{.25in}}\), 36, -108, \(\underline{\hspace{.25in}}\)
5. \(\underline{\hspace{.25in}}\), 12, 18, 27, \(\underline{\hspace{.25in}}\)

The first term of a sequence is 4.

1. Choose a growth factor, and list the next 3 terms of a geometric sequence.
2. Choose a different growth factor, and list the next 3 terms of a geometric sequence.

Here is a rule that can be used to build a sequence of numbers once a starting number is chosen: Each number is two times three less than the previous number. 

1. Starting with the number 0, build a sequence of 5 numbers.
2. Starting with the number 3, build a sequence of 5 numbers.
3. Can you choose a starting point so that the first 5 numbers in your sequence are all positive? Explain your reasoning.