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Thread: How do I interpret the recursive rule and the explicit rule using function notation?

  1. #1

    How do I interpret the recursive rule and the explicit rule using function notation?

    Interpret the recursive rule and the explicit rule using function notation:
    a) Recursive Rule f(n)=f(n-1)*r, f(1)=?
    b) Explicit Rule f(n)=f(1)*r^n-1

    Example: Identify the first term and the common ratio of each geometric sequence:
    c) f(n)=f(n-1)*5, f(1)=-3
    d) f(n)= -2(1/3)^n-1
    Last edited by stapel; 02-10-2018 at 05:59 PM. Reason: Copying question from subject line into post.

  2. #2
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    Quote Originally Posted by BooBooKitty View Post
    a) Recursive Rule f(n)=f(n-1)*r, f(1)=?
    b) Explicit Rule f(n)=f(1)*r^n-1

    Example: Identify the first term and the common ratio of each geometric sequence:
    c) f(n)=f(n-1)*5, f(1)=-3
    d) f(n)= -2(1/3)^n-1
    It's not clear what the question is, or even whether c and d are meant to be part of the question, or an example of something.

    Please state more fully what you are supposed to do here, and what thoughts you have about it. What have you learned about recursive and explicit rules, and what is it that you don't understand? (The more words you use, the better, up to a point!)

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    Quote Originally Posted by BooBooKitty View Post
    a) Recursive Rule f(n)=f(n-1)*r, f(1)=?
    b) Explicit Rule f(n)=f(1)*r^n-1

    Example: Identify the first term and the common ratio of each geometric sequence:
    c) f(n)=f(n-1)*5, f(1)=-3
    d) f(n)= -2(1/3)^n-1
    Like Dr. Peterson, I am not sure what you are asking. But perhaps what you are asking for is an explanation of the difference between an explicit rule and a recursive rule.

    Let's start with "function": it means a kind of rule. We could make a more rigorous definition, but in terms of ease of comprehension, "rule" works for now. A function represents a number that is fully determined by a rule applied to an ordered set of numbers. The number that results from the rule is called the dependent variable. The variable (or variables) that are used by the rule is (are) called the independent variable (variables).

    When we talk about the "explicit rule" and the "recursive rule," we are talking about two different rules that have the exact same effect. Just as Robert and Bob can refer to the same person, when we talk about an explicit and a recursive rule for a function, we are talking about one function that can be described by two seemingly different rules.

    Does that help?
    Last edited by JeffM; 02-06-2018 at 11:08 AM.

  4. #4
    Quote Originally Posted by JeffM View Post
    Like Dr. Peterson, I am not sure what you are asking. But perhaps what you are asking for is an explanation of the difference between an explicit rule and a recursive rule.

    Let's start with "function": it means a kind of rule. We could make a more rigorous definition, but in terms of ease of comprehension, "rule" works for now. A function represents a number that is fully determined by a rule applied to an ordered set of numbers. The number that results from the rule is called the dependent variable. The variable (or variables) that are used by the rule is (are) called the independent variable (variables).

    When we talk about the "explicit rule" and the "recursive rule," we are talking about two different rules that have the exact same effect. Just as Robert and Bob can refer to the same person, when we talk about an explicit and a recursive rule for a function, we are talking about one function that can be described by two seemingly different rules.

    Does that help?
    JeffM:

    Questions A and B are their own part. And C and D are their own part as well. I just put the two questions together. So question A and B are for the title, while C and D are for the question given above it, (If this makes sense at all).

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    Quote Originally Posted by BooBooKitty View Post
    JeffM:

    Questions A and B are their own part. And C and D are their own part as well. I just put the two questions together. So question A and B are for the title, while C and D are for the question given above it, (If this makes sense at all).
    No. I am confused. Please give the complete and exact description of the problem.

  6. #6
    Elite Member stapel's Avatar
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    Cool

    Quote Originally Posted by BooBooKitty View Post
    Interpret the recursive rule and the explicit rule using function notation:
    a) Recursive Rule f(n)=f(n-1)*r, f(1)=?
    b) Explicit Rule f(n)=f(1)*r^n-1

    Example: Identify the first term and the common ratio of each geometric sequence:
    c) f(n)=f(n-1)*5, f(1)=-3
    d) f(n)= -2(1/3)^n-1
    Quote Originally Posted by BooBooKitty View Post
    Questions A and B are their own part. And C and D are their own part as well. I just put the two questions together. So question A and B are for the title, while C and D are for the question given above it...
    I have copied (a portion of) the subject line, which you seem to state is actually the instructions for the first two "questions" (listed as "a" and "b", but which you refer to as "A" and "B"), into your first post, and have positioned the text as being the instructions. Have I edited your first post correctly?

    When the "instructions" for "a" (or "A") say to "intepret the recursive rule...using function notation", why does the "question" ask only for the value of "f(1)", rather than for "f(n)"? Or is the "f(1)=?" portion a second part to the first question?

    For "b" (or "B"), is the "minus one" part of the power on "r", or does it come after?

    For "c" (or "C"), you are given the first term for the geometric sequence. You know how to get from one term to the next in any geometric sequence, given the previous term and the common ratio. You are given a rule for getting from one term to the next term, given the previous term. What then must be the common ratio?

    For "d" (or "D"), is the "minus one" part of the power with the "n", or does it come after?

    For all parts, please reply with your thoughts and efforts so far, as this will likely help us greatly in figuring out what is going on here. Thank you!

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