Results 1 to 3 of 3

Math Help - Arithmetic sequence

  1. #1
    Newbie
    Joined
    Feb 2009
    Posts
    7

    Arithmetic sequence

    The first term of an arithmetic sequence is 30 and the common differenc eis -1.5.
    a) Find the value of the 25th term.

    The rth term of the sequence is 0.
    b)Find the value of r.

    The sum of the first n terms of the sequence is Sn.

    c) Find the largest postitive value of Sn.

    i worked out a and b but got stuck with c. Any help!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    -1
    e^(i*pi)'s Avatar
    Joined
    Feb 2009
    From
    West Midlands, England
    Posts
    3,053
    Thanks
    1
    Quote Originally Posted by thereddemon View Post
    The first term of an arithmetic sequence is 30 and the common differenc eis -1.5.
    a) Find the value of the 25th term.

    The rth term of the sequence is 0.
    b)Find the value of r.

    The sum of the first n terms of the sequence is Sn.

    c) Find the largest postitive value of Sn.

    i worked out a and b but got stuck with c. Any help!
    Part c will be the sum of terms from the first term to your answer to part b which will be the sum of all the positive terms hence the most positive
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,548
    Thanks
    539
    Hello, thereddemon!

    Another approach . . .


    The first term of an arithmetic sequence is a = 30
    . . and the common difference is d = \text{-}1.5

    The sum of the first n terms of the sequence is S_n.

    c) Find the largest postitive value of S_n.
    Formula: . S_n \;=\;\frac{n}{2}\bigg[2a + (n-1)d\bigg]


    We have: . a = 30,\;d = \text{-}1.5

    . . S \:=\:\frac{n}{2}\bigg[2(30) + n(-1.5)\bigg] \quad\Rightarrow\quad S \:=\:30n - 0.75n^2

    This is a down-opening parabola; its maximum is at its vertex.

    . . The vertex is at: . n \:=\:\frac{\text{-}b}{2a} \:=\:\frac{\text{-}30}{2(\text{-}0.75)} \:=\:20


    Therefore, maximim S is: . S \:=\:30(20)+0.75(20^2) \;=\;300

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Arithmetic Sequence
    Posted in the Algebra Forum
    Replies: 4
    Last Post: April 21st 2011, 11:27 PM
  2. Replies: 2
    Last Post: August 24th 2010, 02:10 AM
  3. Arithmetic Sequence help!
    Posted in the Algebra Forum
    Replies: 2
    Last Post: March 15th 2009, 05:34 PM
  4. Arithmetic Sequence
    Posted in the Algebra Forum
    Replies: 1
    Last Post: November 19th 2008, 02:10 PM
  5. Replies: 12
    Last Post: November 15th 2006, 12:51 PM

Search Tags


/mathhelpforum @mathhelpforum