Answer:
The sequence is geometric.
Step-by-step explanation:
Arithmetic Sequence:
A arithmetic sequence is a sequence of numbers in which the next term is calculated by adding some constant amount to the current term. It can be seen almost as a linear equation, but "x" is always a whole number, that starts at zero and increases by one.
We can check if a sequence is arithmetic or not, by subtracting any term from the next term. This amount should be constant for all terms if a sequence is arithmetic. This constant amount can be seen as the slope, how much it's changing by each term.
Geometric Sequence:
A geometric sequence is a sequence of numbers in which the next term is calculated by multiply by some constant amount and the current term. It can be seen almost as a exponential equation, but "x" is always a whole number, that starts at zero and increases by one.
Using the definition above, it can also be thought of as the current term being equal to the previous term multiplied by a constant amount. This means if we divide any term in the sequence by the previous term, this should be a constant amount, no matter which term we use.
Now that we know what the definitions of a geometric and arithmetic sequence as well as how to check if a sequence is either, we can now apply this knowledge to the problem. Let's start by checking if the sequence is arithmetic.
We can start by using the first term "45" and subtracting it from the second term "15", which gives us "-30". This means we had to "add" "-30" to get the second term. If this sequence is arithmetic, this means we could add this to the second term and get the third term. If we add "-30" to "15" we get "-15" which is not equal to the next term. So the amount that it's changing by is not constant, meaning this sequence is not arithmetic.
Now let's check if the sequence is geometric. Each term can be defined as the previous term multiplied by some constant amount. So if we divide any term by it's previous term we get this amount that it had to be multiplied by which should be constant. We cannot start with the first term, since there is no previous term before the first term. So let's start with the second term: "15", now let's divide it by the previous term, which is the first term: "45" [tex]\frac{15}{45} = \frac{1}{3}[/tex]. If this sequence is geometric, we can multiply the second term by this 1/3 and get the next term, which is the third term. If we multiply "15" (the second term) by "1/3" we get [tex]\frac{15}{3}[/tex] which is equal to "5", which is equal to the third term. So this sequence appears to be geometric.
