Is there a common difference or a common ratio between consecutive terms?
B
b
Is there a common difference or a common ratio between consecutive terms?
C
c
Is there a common difference or a common ratio between consecutive terms?
D
d
Is there a common difference or a common ratio between consecutive terms?
A
a
Sequence: Exponential
Common Ratio: 12
B
b
Sequence: Linear
Common Difference: 5
C
c
Other
D
d
Sequence: Exponential
Common Ratio: 1.5
Practice makes perfect
a
We will begin by explaining the difference between a linear and exponential sequence. Note that an exponential sequence is the same thing as a geometric sequence.
If a sequence is linear, there is a common difference between consecutive terms.
If a sequence is geometric, there is a common ratio between consecutive terms.
Let's start by investigating if it is linear.
Since the difference between consecutive numbers is not constant, this is not a linear sequence. By dividing the second number by the first and the third by the second, we can investigate if the sequence increases exponentially.
144/12 =12 1728/144=12
The sequence increases exponentially with a common ratio of 12.
b
Like in Part A, we will examine the differences between consecutive numbers.
This sequence is linear with a constant of 5.
c
Like in Parts A and B, we will examine the difference between consecutive numbers.
The sequence is not linear. Note that we can immediately say that it is not geometric either, because the first term is 0 and you cannot divide or multiply with any number and get 0.
d
Like in Parts A through C, we have to examine if the sequence is linear.
The sequence is not linear, so we proceed by investigating if it is geometric.
The sequence is geometric, with a common difference of 1.5.
