Results 1 to 2 of 2

Math Help - arithmetic sequences

  1. #1
    Super Member
    Joined
    Sep 2008
    Posts
    607

    arithmetic sequences

    A polygon has 10 sides. The lengths of the sides, starting with the smallest, form an arithmetic series. The perimeter of the polygon is 675 cm and the length of the longest side is twice that of the shortest side. Find, for this series:

    (a) The common difference.

    (b) The first term.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Jester's Avatar
    Joined
    Dec 2008
    From
    Conway AR
    Posts
    2,340
    Thanks
    21
    Quote Originally Posted by Tweety View Post
    A polygon has 10 sides. The lengths of the sides, starting with the smallest, form an arithmetic series. The perimeter of the polygon is 675 cm and the length of the longest side is twice that of the shortest side. Find, for this series:

    (a) The common difference.

    (b) The first term.
    Let a be the shortest side and d the difference so the sides are

    a, a+d, a+2d,\; \cdots \; a + 9d

    Adding gives 10a + 45d = 675\, (*), the condition that the longest is twice the shortes gives 2a = a + 9d or a = 9d. Use this in (*).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Arithmetic Sequences
    Posted in the Algebra Forum
    Replies: 1
    Last Post: April 17th 2009, 11:36 PM
  2. Replies: 2
    Last Post: February 18th 2009, 07:14 AM
  3. arithmetic of sequences
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 26th 2008, 03:34 PM
  4. Arithmetic sequences- please help!
    Posted in the Algebra Forum
    Replies: 1
    Last Post: November 25th 2008, 07:23 AM
  5. Arithmetic Sequences
    Posted in the Algebra Forum
    Replies: 4
    Last Post: June 14th 2008, 07:46 PM

Search Tags


/mathhelpforum @mathhelpforum