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Math Help - Recursive Formulas & Sequences

  1. #1
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    Exclamation Recursive Formulas & Sequences

    Directions tell me to provide a recursive formula for the sequence and to specify what type of sequence it is.

    1] 1,1,2,3,5,8

    2] 5,10, 20, 40, 80, 160

    I understand the patterns & how they derived the terms, but I can't figure out how to write the recursive formula. Help, please & thank you.

    *Detailed instructions, if possible, please.
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  2. #2
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    Quote Originally Posted by helpme View Post
    Directions tell me to provide a recursive formula for the sequence and to specify what type of sequence it is.

    1] 1,1,2,3,5,8

    2] 5,10, 20, 40, 80, 160

    I understand the patterns & how they derived the terms, but I can't figure out how to write the recursive formula. Help, please & thank you.

    *Detailed instructions, if possible, please.
    For 1) what is 1 + 1?

    What is 1 + 2?

    What is 2 + 3?

    What is 3 + 5?


    Can you see that each term is the sum of the two that preceded it?

    So f_{n + 2} = f_{n + 1} + f_n

    This is called the Fibonnaci Sequence.

    Note: There is actually a term missing. It should be 0, 1, 1, 2, 3, 5, 8, ...



    2) What is 5 x 2?

    What is 10 x 2?

    What is 20 x 2?

    Can you see that each term is the previous term multiplied by 2?

    So f_{n + 1} = 2f{n}.
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  3. #3
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    Quote Originally Posted by Prove It View Post
    For 1) what is 1 + 1?

    What is 1 + 2?

    What is 2 + 3?

    What is 3 + 5?


    Can you see that each term is the sum of the two that preceded it?

    So f_{n + 2} = f_{n + 1} + f_n

    This is called the Fibonnaci Sequence.

    Note: There is actually a term missing. It should be 0, 1, 1, 2, 3, 5, 8, ...



    2) What is 5 x 2?

    What is 10 x 2?

    What is 20 x 2?

    Can you see that each term is the previous term multiplied by 2?

    So f_{n + 1} = 2f{n}.

    for number 2. it's a geometric sequence right?
    & my common ratio is 2...
    so I can write my formula as An = 2An-1 ?

    thanks, btw.
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  4. #4
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    Quote Originally Posted by helpme View Post
    for number 2. it's a geometric sequence right?
    & my common ratio is 2...
    so I can write my formula as An = 2An-1 ?

    thanks, btw.
    Yes it's a geometric sequence.

    And yes, writing A_n = 2A_{n - 1} is fine.
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