Jake has proven that a function, f(x), is a geometric sequence. How did he prove that?
- He showed that an explicit formula can be created
- He showed that a recursive formula could be created
- He showed that f(n)/f(n-1) was a constant ratio**
- He showed that f(n)-f(n-1) was a constant difference
I'm not so sure on my answer. If its wrong, could someone explain to me how to do the problem, I'm very confused. Thank you!
You selected the correct answer: "He showed that f(n)/f(n-1) was a constant ratio".
To prove that a function f(x) is a geometric sequence, one needs to establish that the ratio of any term to its preceding term is constant.
Specifically, Jake demonstrated that the ratio of f(n) to f(n-1) remains constant. This means that for any value of n, the ratio of f(n)/f(n-1) will always be the same value. This is a crucial characteristic of a geometric sequence and provides evidence for its identification.
The other options you listed, regarding explicit formulas, recursive formulas, and constant differences, are not directly related to proving a function to be a geometric sequence. They may be relevant in analyzing and describing the sequence further but are not the primary means of demonstrating the geometric nature of the sequence.
If you have any further questions or need clarification, please let me know.