Consider the sequence that begins $40, 20, 10, 5, …$

1. Based on the information given, can this sequence be arithmetic? Can it be geometric? Why?

   Hint (a):

   Read the Math Notes box in Lesson 5.3.2.

2. Assume this is a geometric sequence. On graph paper, graph the sequence up to $n = 6$.

   Hint (b):

   Start by making a table of values.

3. Will the values of the sequence ever become zero or negative? Explain.

   Answer (c):

   No. Multiplying by $0.5$ will never yield $0$ unless the other factor is $0$, which is impossible in this sequence.
   When multiplying two positive numbers, a negative number can never be obtained.