Results 1 to 13 of 13

Math Help - Adding terms

  1. #1
    Junior Member
    Joined
    May 2010
    Posts
    43

    Adding terms

    Can someone help me find the sum of the first 19 terms of the following sequence?



    -11, -8, -5 . . .
    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 tysonrss View Post
    Can someone help me find the sum of the first 19 terms of the following sequence?



    -11, -8, -5 . . .
    It is an arithmetic sequence with first term (a) -11 and common difference (d) 3 and you want to find S_{19}


    The sum of an arithmetic sequence is given by S_n = \frac{n}{2}[2a+(n-1)d]
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,969
    Thanks
    1788
    Awards
    1
    Quote Originally Posted by tysonrss View Post
    Can someone help me find the sum of the first 19 terms of the following sequence?
    -11, -8, -5 . . .
    \sum\limits_{k = 0}^{18} {\left( { - 11 + 3k} \right)}  = \left( { - 11} \right)\left( {19} \right) + 3 \cdot \frac{{18 \cdot 19}}{2}
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    May 2010
    Posts
    43
    So it'd be 171?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor harish21's Avatar
    Joined
    Feb 2010
    From
    Dirty South
    Posts
    1,036
    Thanks
    10
    Quote Originally Posted by tysonrss View Post
    So it'd be 171?
    what? how did you get 171? please look at what plato has told you to do

    (-11 \times 19 ) + \left(3 \times \frac{18 \times 19}{2} \right)

    = -209 + 513
    Last edited by harish21; May 22nd 2010 at 10:42 AM.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Senior Member nikhil's Avatar
    Joined
    Jun 2008
    Posts
    292

    Lightbulb here is the general solution

    use arithmetic progression
    Last edited by nikhil; May 22nd 2010 at 10:49 AM.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor harish21's Avatar
    Joined
    Feb 2010
    From
    Dirty South
    Posts
    1,036
    Thanks
    10
    Quote Originally Posted by nikhil View Post
    let get the general solution by which particular solution can be obtained.
    let there b n terms with t(n) as the nth term. let
    s=(-11)+(-8)+(-5)+....................................+t(n) (1)
    s= ____(-11)+(-8)+(-5)+..............................+t(n) (2)(shift right by 1 term)
    subtracting 2 from 1 we have
    0=-11+3+3+3+..................................-t(n) or
    t(n)=-11+3+3+....n-1 times therefor
    t(n)=-11+3(n-1) or
    t(n)=3n-14
    now we are suppose to add t(1),t(2) till t(n) therefor
    S(t(n))=S(3n)-S(14) S stands for summation
    S(t(n))=3[(n(n+1))/2]-14n.................(after operating summation)
    now for particular solution put n=19
    S(t(19))=3(19)(10)-126=444
    therefor solution is 444
    Nikhil,

    your notation is a little hard to understand, but 444 is not the correct answer!
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Junior Member
    Joined
    May 2010
    Posts
    43
    304 is the answer?
    Follow Math Help Forum on Facebook and Google+

  9. #9
    MHF Contributor harish21's Avatar
    Joined
    Feb 2010
    From
    Dirty South
    Posts
    1,036
    Thanks
    10
    Quote Originally Posted by tysonrss View Post
    304 is the answer?
    Yes!!
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Senior Member nikhil's Avatar
    Joined
    Jun 2008
    Posts
    292

    two ways

    final equation is
    3[(n(n+1))/2]-14n
    put n=19
    so answer is
    3(19)(10)- 14(19)
    570-266=304
    also
    using arithmatic progression
    s=(n/2)[2a+(n-1)d]
    here d=3,n=19,a=-11
    s=(19)[-11+27]=19x16=304
    I did calculation mistake(put 14(9) instead of 14(19)) that I realised after posting. I edited it but you being so fast quoted my previous answer which had a mistake
    I gave the complex method because it can also be used to find sum to n terms of series like 1+3+6+10 and so on...
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Junior Member
    Joined
    May 2010
    Posts
    43
    Quote Originally Posted by harish21 View Post
    Yes!!
    Can you break it down how you got that equation, yours seem a bit more understandable than the others posted here and I need to know how to use that equation for the other problems.
    Follow Math Help Forum on Facebook and Google+

  12. #12
    MHF Contributor harish21's Avatar
    Joined
    Feb 2010
    From
    Dirty South
    Posts
    1,036
    Thanks
    10
    Quote Originally Posted by tysonrss View Post
    Can you break it down how you got that equation, yours seem a bit more understandable than the others posted here and I need to know how to use that equation for the other problems.
    look at this to understand arithmetic sequences. Also look for arithmetic series in the same page. You should be able to understand how you can solve this problem.
    Follow Math Help Forum on Facebook and Google+

  13. #13
    Junior Member
    Joined
    May 2010
    Posts
    43
    Quote Originally Posted by harish21 View Post
    look at this to understand arithmetic sequences. Also look for arithmetic series in the same page. You should be able to understand how you can solve this problem.
    Thanks, I already figuired it out
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Prove that adding one to itself is always different from 0
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: January 12th 2010, 04:09 AM
  2. Adding partitions.
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: March 22nd 2009, 08:13 AM
  3. matrix addition question on adding the unknown terms
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: March 20th 2009, 09:42 PM
  4. Adding
    Posted in the Algebra Forum
    Replies: 2
    Last Post: March 20th 2009, 02:29 AM
  5. Adding Pi.
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: October 14th 2008, 12:48 PM

Search Tags


/mathhelpforum @mathhelpforum