Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    9
    ReputationRep:
    The sum of the first n terms of a series is n(n+2). Find the first three terms of the series.


    I don't have a clue! All I've got is sn=n(n+2)
    Offline

    19
    ReputationRep:
    (Original post by Lucofthewoods)
    The sum of the first n terms of a series is n(n+2). Find the first three terms of the series.


    I don't have a clue! All I've got is sn=n(n+2)
    Use the formula for the term of the first n terms of a series, and you're given to find the first three terms so when n=3. Put it in your formula to get the answer.
    Offline

    11
    ReputationRep:
    (Original post by Lucofthewoods)
    The sum of the first n terms of a series is n(n+2). Find the first three terms of the series.


    I don't have a clue! All I've got is sn=n(n+2)
    Let the nth term of your series be given by u_n and the sum of the first n terms be S_n.
    Note that: S_1=u_1.

    You know a formula for S_n. So if you sub in n=1 you can find u_1.

    What can you say about S_2 and its relation to S_1 and u_2?
    What about S_3?
    Offline

    10
    ReputationRep:
    (Original post by Lucofthewoods)
    The sum of the first n terms of a series is n(n+2). Find the first three terms of the series.


    I don't have a clue! All I've got is sn=n(n+2)
    Call your arithmetic progression  a_n .  a_1 = a ,  a_2 = a + d ,  a_3 = a+2d ,  a_n = a + (n-1)d . The partial sums of this progression, aka the sum of the first n terms, is found by adding up the first n terms of our arithmetic progression.  a_1 + a_2 + a_3 + a_4 + ... + a_n this can be compacted by using sigma notation  \sum\limits_{n=1}^n a_n = a_1 + a_2 + a_3 + a_4 + ... + a_n . We are told what the sum of the first  n terms of our progression is  n(n+2) . So,  S_n= \sum\limits_{n=1}^n a_n = n(n+2)

    Notice, that when  n = 1,2,3

     S_1 = \sum\limits_{n=1}^1 a_n = a_1
     S_2 = \sum\limits_{n=1}^2 a_n = a_1 + a_2
     S_3 = \sum\limits_{n=1}^3 a_n = a_1 + a_2 + a_3

    You now need to find,  a_1, a_2 and  a_3 . Good luck, I hope what I've said helps.
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    What newspaper do you read/prefer?
    Useful resources

    Make your revision easier

    Maths

    Maths Forum posting guidelines

    Not sure where to post? Read the updated guidelines here

    Equations

    How to use LaTex

    Writing equations the easy way

    Student revising

    Study habits of A* students

    Top tips from students who have already aced their exams

    Study Planner

    Create your own Study Planner

    Never miss a deadline again

    Polling station sign

    Thinking about a maths degree?

    Chat with other maths applicants

    Can you help? Study help unanswered threads

    Groups associated with this forum:

    View associated groups
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

    Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

    Quick reply
    Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.