Is their a common difference between consecutive terms? How about a common ratio?
B
b
Use the common ratio you found in Part A to find the fifth and sixth term.
C
c
Multiplying by 0.5 is the same thing as dividing by 2.
A
a
Geometric. See solution.
B
b
Diagram:
C
c
No, see solution.
Practice makes perfect
a
If the sequence is arithmetic, there should be a common difference between consecutive terms. Let's investigate.
As we can see, there is not a common difference between consecutive terms and therefore, this cannot be an arithmetic sequence. If the sequence is geometric, there is a common ratio between consecutive terms. Let's try that.
Between consecutive terms there is a common ratio of 0.5. Therefore, this is a geometric sequence.
b
Using the common ratio of 0.5, we can find the fifth and sixth term.
Now we can plot the sequence.
Note that we should not connect the terms.
c
To go from one term to the next we have to multiply by 0.5, which is the same thing as dividing by 2. When we divide something by 2 the quotient will always be half of what it was before. Since the numerator is always positive, the quotient will always be positive. Therefore, the sequence will never be 0 or negative.
