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

    6
    ReputationRep:
    a couple quick questions!;


    what's the nth term for this sequence? I'm struggling as there's (I don't think) no common ratio (and so can't use the formula ar^(n-1) and it's surely not an AP either?
    4, 9, 16, 25, ...

    and a bit stuck with this one;

    how do I simplfy (into a single log);
    logx+logx^2

    just unsure if I do
    logx+2logx = 3logx
    or
    times the x^2 by the x, and so =logx^3 ?

    many thanks
    • TSR Support Team
    • Study Helper
    Offline

    20
    ReputationRep:
    (Original post by m1800)
    a couple quick questions!;


    what's the nth term for this sequence? I'm struggling as there's (I don't think) no common ratio (and so can't use the formula ar(n-1) and it's surely not an AP either?
    4, 9, 16, 25, ...

    and a bit stuck with this one;

    how do I simplfy (into a single log);
    logx+logx^2

    just unsure if I do
    logx+2logx = 3logx
    or
    times the x^2 by the x, and so =logx^3 ?

    many thanks
    No it's not an AP. Do you recognise these numbers?

    3logx and log x^3 are the same thing so either is fine.
    Offline

    9
    ReputationRep:
    (Original post by m1800)
    what's the nth term for this sequence? I'm struggling as there's (I don't think) no common ratio (and so can't use the formula ar(n-1) and it's surely not an AP either?
    4, 9, 16, 25, ...
    You are correct that this is not a geometric or arithmetic sequence. You are expected to notice something - these are numbers that you should recognise. If I tell you that the term before the 4 is 1, and the term after the 25 is 36, does that help?

    (Original post by m1800)
    how do I simplfy (into a single log);
    logx+logx^2

    just unsure if I do
    logx+2logx = 3logx
    or
    times the x^2 by the x, and so =logx^3 ?
    It looks like you have used the relationship log(x^n) = n log(x) to turn log(x^2) into 2 log (x), so you can use this same law to see that your two suggestions are equivalent. If you are asking which form they will be expecting, I don't think it really matters. Although there might be a case for saying that log(x^3) is a single logarithm, rather than three times a single logarithm, but I think that's a bit overly pedantic.
    Offline

    18
    ReputationRep:
    For the sequence, try taking the differences between each term and then finding the second-order differences (the differences of the differences). Those should be constant. Do you remember doing quadratic sequences at GCSE?

    As for the log, remember that log(x^2) (I'm assuming that's what you meant) is 2logx.
    • Thread Starter
    Offline

    6
    ReputationRep:
    (Original post by Notnek)
    No it's not an AP. Do you recognise these numbers?

    3logx and log x^3 are the same thing so either is fine.
    (Original post by Pangol)
    It looks like you have used the relationship log(x^n) = n log(x) to turn log(x^2) into 2 log (x), so you can use this same law to see that your two suggestions are equivalent. If you are asking which form they will be expecting, I don't think it really matters. Although there might be a case for saying that log(x^3) is a single logarithm, rather than three times a single logarithm, but I think that's a bit overly pedantic.

    oh so it's correct? thanks guys.

    (Original post by Pangol)
    You are correct that this is not a geometric or arithmetic sequence. You are expected to notice something - these are numbers that you should recognise. If I tell you that the term before the 4 is 1, and the term after the 25 is 36, does that help?

    (Original post by Notnek)
    No it's not an AP. Do you recognise these numbers?

    (Original post by TheMindGarage)
    For the sequence, try taking the differences between each term and then finding the second-order differences (the differences of the differences). Those should be constant. Do you remember doing quadratic sequences at GCSE?
    still lost :l

    So the difference is of course increasing by two each time, i just have no idea how to put this into a formula :l
    Offline

    18
    ReputationRep:
    (Original post by m1800)
    still lost :l

    So the difference is of course increasing by two each time, i just have no idea how to put this into a formula :l
    The formula for the nth term is in the format an^2 + bn + c

    The second-order difference is 2, so a is equal to half of that or 1 (don't ask why...).

    So now you have n^2 + bn + c. Substitute in two values (for example, n=1 and n=2):

    1+b+c = 4
    4+2b+c = 9

    Now just solve as a normal pair of simultaneous equations.
    • Thread Starter
    Offline

    6
    ReputationRep:
    (Original post by TheMindGarage)
    The formula for the nth term is in the format an^2 + bn + c

    The second-order difference is 2, so a is equal to half of that or 1 (don't ask why...).

    So now you have n^2 + bn + c. Substitute in two values (for example, n=1 and n=2):

    1+b+c = 4
    4+2b+c = 9

    Now just solve as a normal pair of simultaneous equations.
    ok so b=2 and c=1 so whats the formula? :l

    sorry ive never come across this method inc. at GCSE

    to me this just seems like a very odd question altogether
    Offline

    9
    ReputationRep:
    (Original post by m1800)
    ok so b=2 and c=1

    sorry ive never come across this method inc. at GCSE

    to me this just seems like a very odd question altogether.
    This may be a valid method (I haven't read the details), I am sure that the idea of this question is to just notice a pattern, one that should be very familiar to you. 1 4 9 16 25 36 49 ...
    • Thread Starter
    Offline

    6
    ReputationRep:
    (Original post by Pangol)
    This may be a valid method (I haven't read the details), I am sure that the idea of this question is to just notice a pattern, one that should be very familiar to you. 1 4 9 16 25 36 49 ...
    oh lord help me

    of course it's square numbers

    I need to sleep

    thanks a lot guys
    Offline

    18
    ReputationRep:
    (Original post by Pangol)
    This may be a valid method (I haven't read the details), I am sure that the idea of this question is to just notice a pattern, one that should be very familiar to you. 1 4 9 16 25 36 49 ...
    You could do that, and then you'd get (n-1)^2 since the actual sequence starts with 4 rather than 1.
    Offline

    9
    ReputationRep:
    (Original post by TheMindGarage)
    You could do that, and then you'd get (n-1)^2 since the actual sequence starts with 4 rather than 1.
    Yes, I know that. This was my second post on this thread gently nudging the OP towards noticing the pattern, and I had already indicated that I was adding a term on the beginning as well as a few on the end.
    Online

    17
    ReputationRep:
    (Original post by Pangol)
    Although there might be a case for saying that log(x^3) is a single logarithm, rather than three times a single logarithm, but I think that's a bit overly pedantic.
    If I had to choose, definitely 3 log x beats log x^3. Easier to evaluate, easier expression to differentiate/integrate, etc...

    [Not that it really matters, of course! ]
 
 
 
  • 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.