Turn on thread page Beta

Arithmetic series watch

Announcements
    • Thread Starter
    Offline

    12
    ReputationRep:
    Prove that if one arithmetic series has 1 square and one cube, it will has one term is the power of six of an integer.
    Offline

    15
    ReputationRep:
    (Original post by BCHL85)
    Prove that if one arithmetic series has 1 square and one cube, it will has one term is the power of six of an integer.
    Without any loss of generality one can start the arithmetic progression from the square. Call this first term a^2 and call the common difference d.

    Then for some k and some b

    a+kd=b^3

    So, squaring

    a^2 + (2ka+dk^2)d =b^6

    which is the (2ka+dk^2-1)th term in the AP.
    Offline

    1
    ReputationRep:
    But it isnt the same AP as the one with the cube term. They have different first terms.
    Offline

    15
    ReputationRep:
    (Original post by JamesF)
    But it isnt the same AP as the one with the cube term. They have different first terms.
    You're right - wasn't thinking!
    Offline

    1
    ReputationRep:
    (Original post by JamesF)
    But it isnt the same AP as the one with the cube term. They have different first terms.
    What do you mean? The question says one AP.
    Offline

    15
    ReputationRep:
    (Original post by J.F.N)
    What do you mean? The question says one AP.
    I started one of my APs with term a, one with a^2 - that was my error.
    • Thread Starter
    Offline

    12
    ReputationRep:
    There are some questions relate to that
    - If a arithmetic series has one square. Prove that there's another one in this series.
    - 2nd is like I posted.
    - If a arithmetic series has 3 terms are the powers of 2, 3, 5. Prove that there's a term is power of 2.3.5 = 30.
    - If it has n terms are the powers of n numbers, every couples are prime number with each other. Prove that there's a term is the power of multiplication of these numbers.
    Woa ... hard to express the general question.
 
 
 
Turn on thread page Beta
Updated: February 2, 2005

University open days

  • University of the Arts London
    MA Performance Design and Practice Open Day Postgraduate
    Thu, 24 Jan '19
  • Brunel University London
    Undergraduate Experience Days Undergraduate
    Sat, 26 Jan '19
  • SOAS University of London
    Postgraduate Open Day Postgraduate
    Sat, 26 Jan '19
Poll
Are you chained to your phone?
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.