Results 1 to 2 of 2

Math Help - series and sequences question

  1. #1
    Newbie
    Joined
    Sep 2008
    Posts
    3

    series and sequences question

    The sum of the first two terms of an arithmetic series is 47.
    The thirtieth term of this series is -62. Find the first term of the series and the common difference.
    I'm stuck on the first bit. I'm not quite sure how to work out which two terms equal the sum of 47....thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6
    Hello,
    Quote Originally Posted by girlpower1991 View Post
    The sum of the first two terms of an arithmetic series is 47.
    The thirtieth term of this series is -62. Find the first term of the series and the common difference.
    I'm stuck on the first bit. I'm not quite sure how to work out which two terms equal the sum of 47....thanks.
    Let \delta be the common difference and a_1, ~a_2,~\text{etc} the terms of the series.

    a_2=a_1+ \delta

    But we know that a_1+a_2=47

    Thus 2a_1+ \delta=47

    The thirtieth term is -62=a_{30}=a_1+29 \delta

    So we have the system :

    \left\{\begin{array}{ll} 2a_1+\delta=47 \quad (1) \\ a_1+29 \delta=-62 \quad (2) \end{array} \right.

    2*(2)-(1) ~:~ 2(a_1+29 \delta)-(2a_1+\delta)=2*(-62)-47

    The a_1 simplify and we get :
    58 \delta- \delta=-124-47

    57 \delta=-171

    \boxed{\delta=-3}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Sequences and Series Question
    Posted in the Advanced Math Topics Forum
    Replies: 4
    Last Post: July 14th 2011, 06:06 AM
  2. Sequences and series question.
    Posted in the Calculus Forum
    Replies: 4
    Last Post: October 11th 2010, 07:47 AM
  3. Sequences and Series - Power Series Question
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 20th 2008, 07:32 PM
  4. Another Question regarding Sequences and Series
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: September 10th 2007, 10:13 AM
  5. Sequences/Series question
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 1st 2005, 12:39 PM

Search Tags


/mathhelpforum @mathhelpforum