Results 1 to 4 of 4

Math Help - Sequences

  1. #1
    Junior Member Dragon's Avatar
    Joined
    Oct 2006
    Posts
    63

    Sequences

    The terms of some sequences are determined according to the following rule: If the values of a given term t is odd positive integer, then the value next term is 3t-9 if the value of a given term t is an even positive integer then the value next term is 2t-7 if the term of the seuence alternate between two positive integers(a,b,a,b........)what is the sum of two positive integers?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Quick's Avatar
    Joined
    May 2006
    From
    New England
    Posts
    1,024
    Quote Originally Posted by Dragon View Post
    The terms of some sequences are determined according to the following rule: If the values of a given term t is odd positive integer, then the value next term is 3t-9 if the value of a given term t is an even positive integer then the value next term is 2t-7 if the term of the seuence alternate between two positive integers(a,b,a,b........)what is the sum of two positive integers?
    So you have positive integer a and so the next term is: 2a-7

    Then the term after that is: 3(2a-7)-9

    So add a to that: a+3(2a-7)-9

    Then get rid of parenthesis: a+6a-21-9

    Add/Subtract: 7a-30

    And that is as close as you can get.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,678
    Thanks
    611
    Hello, Dragon!

    An interesting problem . . .


    The terms of a sequence are determined according to the following rule:
    If a term t is odd, then the next term is 3t-9.
    If a term t is even, then the next term is 2t-7.

    If the terms of the sequence alternate between two positive integers: a, b, a, b ...
    what is the sum of two positive integers?

    Let a be an odd positive integer.

    Then the next term is: . b \:=\:3a - 9 ... an even integer.

    Then the next term is: . c \:=\:2(3a-9) - 7 \:=\:6a - 25

    But this is equal to the first term a.
    . . Hence, we have: . 6a - 25\:=\:a\quad\Rightarrow\quad\boxed{a\,=\,5}

    Then: . b \:=\:3(5) - 9\quad\Rightarrow\quad\boxed{b\:=\:6}


    Thererfore: . \boxed{a + b \:=\:11}

    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Quick's Avatar
    Joined
    May 2006
    From
    New England
    Posts
    1,024
    I thought it said first two even integers Ignore my answer.

    Quote Originally Posted by Soroban View Post
    But this is equal to the first term a.
    Why?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Convergence in sequences of sequences
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: October 19th 2010, 07:28 AM
  2. Sequences and the sequences' arithmetics
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: October 6th 2010, 09:31 PM
  3. Monotone sequences and Cauchy sequences
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: March 21st 2009, 08:59 PM
  4. Sequences Q3
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 9th 2009, 05:08 AM
  5. Replies: 5
    Last Post: January 16th 2008, 04:51 PM

Search Tags


/mathhelpforum @mathhelpforum