Hey there Sign in to join this conversationNew here? Join for free

nth term of a sequence....

Announcements Posted on
Study Help needs new mods! 14-04-2014
Post on TSR and win a prize! Find out more... 10-04-2014
    • Thread Starter
    • 2 followers
    Offline

    ReputationRep:
    [Edit]
    • 0 followers
    Offline

    ReputationRep:
    Set n = 2k, and consider that -8 = (-2)^3. You should be able to make some progress from there (unless I've made a misunderstanding somewhere).
    • 10 followers
    Offline

    ReputationRep:
    Yeah that sounds right.
    • Thread Starter
    • 2 followers
    Offline

    ReputationRep:
    [Edit]
    • 0 followers
    Offline

    ReputationRep:
    (Original post by flown_muse)
    Okay, now I have:

     a_2_k = \frac{(2k-1)(-2)^3^(^2^k^+^1^)}{2^(^2^k^-^1^)}

    and now I have an issue, because I can't find a value of k that can make both the top and the bottom equal to a power of 4.

    I'm clearly doing something wrong
    Write it as  a_2_k = (2k-1)\frac{(-2)^3^(^2^k^+^1^)}{2^(^2^k^-^1^)}, and remember that -2 = -1 \times 2, so you can expand the powers to get something easier.
    • 10 followers
    Offline

    ReputationRep:
    (Original post by flown_muse)
    Okay, now I have:

     a_2_k = \frac{(2k-1)(-2)^3^(^2^k^+^1^)}{2^(^2^k^-^1^)}

    and now I have an issue, because I can't find a value of k that can make both the top and the bottom equal to a power of 4.

    I'm clearly doing something wrong
    Expand the numerator and simplify.
    • Thread Starter
    • 2 followers
    Offline

    ReputationRep:
    [Edit]
    • 10 followers
    Offline

    ReputationRep:
    (Original post by flown_muse)
     a_2_k = (2k-1)\frac{(-2)^3^(^2^k^+^1^)}{2^(^2^k^-^1^)}
     a_2_k = (2k-1)\frac{(-1)(2)^(^6^k^+^3^)}{2^(^2^k^-^1^)}
     a_2_k = (2k-1).(-1)(2)^(^6^k^+^3^)^-^(^2^k^-^1^)
     a_2_k = (2k-1).(-1)(2)^(^4^k^-^2^)

    etc.?
    What's 3--1?

    Apart from that yeah that's right. You can get rid of the 1 btw.
    • Thread Starter
    • 2 followers
    Offline

    ReputationRep:
    (Original post by f1mad)
    Yeah that's right. You can get rid of the 1 btw.
    So, I have ended up with:

     a_2_k = (2k-1).(-1)(2)^(^4^k^+^4^)
    a_2_k = (1-2k).2^4^k^+^4

    Therefore,  4k+4=4, 4k=0
    • 10 followers
    Offline

    ReputationRep:
    (Original post by flown_muse)
    So, I have ended up with:

     a_2_k = (2k-1).(-1)(2)^(^4^k^+^4^)
    a_2_k = (1-2k).2^4^k^+^4

    Therefore,  4k+4=4, 4k=0
    Hang on, where did the last line come from?
    • Thread Starter
    • 2 followers
    Offline

    ReputationRep:
    (Original post by f1mad)
    Hang on, where did the last line come from?
    Because the question wants me to find An in terms of powers of 4, so I'm setting the power equal to 4.

    (I think?)
    • Thread Starter
    • 2 followers
    Offline

    ReputationRep:
    Oh. I never thought of that. I think you are right, because otherwise I end up with n=0 and the answer is just a number with no powers. Argh! Thanks
    • 10 followers
    Offline

    ReputationRep:
    (Original post by flown_muse)
    Oh. I never thought of that. I think you are right, because otherwise I end up with n=0 and the answer is just a number with no powers. Argh! Thanks
    Yeah you need to re-write it . In terms of 4^ something, since this would then imply powers of 4.

Reply

Submit reply

Register

Thanks for posting! You just need to create an account in order to submit the post
  1. this can't be left blank
    that username has been taken, please choose another Forgotten your password?

    this is what you'll be called on TSR

  2. this can't be left blank
    this email is already registered. Forgotten your password?

    never shared and never spammed

  3. this can't be left blank

    6 characters or longer with both numbers and letters is safer

  4. this can't be left empty
    your full birthday is required
  1. By completing the slider below you agree to The Student Room's terms & conditions and site rules

  2. Slide the button to the right to create your account

    Slide to join now Processing…

    You don't slide that way? No problem.

Updated: March 18, 2012
Article updates
Reputation gems:
You get these gems as you gain rep from other members for making good contributions and giving helpful advice.