Results 1 to 5 of 5

Math Help - geometric sequence question

  1. #1
    Member
    Joined
    May 2008
    Posts
    76

    geometric sequence question

    The first term of a geometric sequence is 27, and the sixth term is 512/9.

    Find the seventh term.

    Find the sum of the first five terms of this sequence.

    My answers are 66.03 and 185.95, am I right?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jun 2008
    Posts
    792
    Yes, you are correct. :-)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    May 2008
    Posts
    76
    Thanks for the confirmation, cause the answer in the book is different. Another typo!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,547
    Thanks
    539
    Hello, cityismine!

    I suspect the typo is in the statement of the problem . . .


    The first term of a geometric sequence is 27, and the sixth term is 1024/9

    (a) Find the seventh term.

    (b) Find the sum of the first five terms of this sequence.
    (a) Formula: .a(n) .= .a(1)r^{n-1}


    We have: .a(1) = 27, . a(6) = 1024/9

    Then: .a(6) = a(1)r^5 . . 1024/9 = 27r^5 . . r^5 = 1024/243

    . . Hence: .r .= .4/3

    Therefore: .a(7) .= .a(6)r .= .(1024/9)(4/3) .= .4096/27


    . . . . . . . . . . . . . . . . . . . r^n - 1
    (b) Formula: .S(n) .= .a(1)---------
    . . . . . . . . . . . . . . . . . . . . r - 1


    . . . . . . . . . . . . . . .(4/3)^5 - 1 . . . 781
    Hence: . S(5) .= .27-------------- .= .-----
    . . . . . . . . . . . . . . . . 4/3 - 1 . . . . . .3


    Were those the answers they expected?

    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    May 2008
    Posts
    76
    Yes sir, those are the answers in the book.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. geometric series/sequence given question
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: July 12th 2010, 01:41 AM
  2. simple geometric sequence question
    Posted in the Algebra Forum
    Replies: 2
    Last Post: November 29th 2009, 09:36 PM
  3. Question about geometric sequence
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: December 15th 2008, 10:59 AM
  4. Infinite geometric sequence question
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: July 26th 2008, 10:11 AM
  5. Geometric Sequence Question...
    Posted in the Algebra Forum
    Replies: 3
    Last Post: February 2nd 2008, 01:12 PM

Search Tags


/mathhelpforum @mathhelpforum