Turn on thread page Beta
    • Thread Starter
    Offline

    0
    ReputationRep:
    The sum of the first two terms of an arithmetic progression is 18 and the sum of the first four terms is 52. Find the suum of the first 8 terms.

    The sum of the first twenty terms of an arithmetic progression is 50, and the sum of the next twenty terms is -50. Find the sum of the first hundred terms of the progression.

    Find the sum of the arithmetic progression 1,4,7,10,13,16....,1000.
    Every third term of the above progression is removed, i.e 7,16 etc. Find the sum of the remaining terms.

    Can anyone tell me step by step how to work it out? Please?
    Offline

    2
    ReputationRep:
    Sum = (n/2)(2a+(n-1)d)

    Sum of 2 terms 2a+d=18
    so 4a+2d=36 (1)

    Sum of 4 terms 2(2a+3d)=52
    so 4a+6d=52 (2)

    subtract (1) from(2)
    gives 4d=16 so d=4
    from(1) 4a+8=36
    so a=7

    sequence is 7, 11, 15, 19

    Sum to 8 terms

    4(14+7.4)=4.42=168

    Try the next one.
    Offline

    2
    ReputationRep:
    The sum of the first twenty terms of an arithmetic progression is 50, and the sum of the next twenty terms is -50. Find the sum of the first hundred terms of the progression.

    Sum to 20 terms: 10(2a+19d)=50
    20a+190d=50
    40a+380d=100 (1)

    Sum to 40 terms: 20(2a+39d) = 0
    40a+780d =0 (2)

    (2)-(1) 400d = -100
    d=-0.25

    from (1) 40a-95=100
    40a=195
    a=4.875

    sum to 100 terms: 50(9.75 +99(-0.25))
    =-750

    Try the last one?
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: February 1, 2006

University open days

  • Heriot-Watt University
    School of Textiles and Design Undergraduate
    Fri, 16 Nov '18
  • University of Roehampton
    All departments Undergraduate
    Sat, 17 Nov '18
  • Edge Hill University
    Faculty of Health and Social Care Undergraduate
    Sat, 17 Nov '18
Poll
Have you ever experienced bullying?
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

Equations

Best calculators for A level Maths

Tips on which model to get

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

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

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