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Solomon E paper question 4 Watch

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    Stuck on C1 Solomon E paper question 4.

    A sequence of terms is defined by:

    Un = 3^n -2

    Write down the first four terms of this sequenc. Done

    b) The same sequence can also be defined by the recurrence relation

    Un 1+1 = aUn +b

    Find the vales of a and b.

    I got the first term correct - that being a+b = 7

    But the second term I got wrong - I got a quadratic and it should be

    7a +b = 25

    Not really sure how you get this .... I substitued what I got for u1 into it but as I say I get a quadractic in a....Help
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    (Original post by christinajane)
    ...
    So, when you plugged n=1 in, you got: (i.e: wherever you see n, you put a 1)

    u_{1+1} = au_{1} + b \iff 7 = a + b

    Now, when you plug n=2 in you get: (i.e: wherever you see n, you put a 2)

    u_{2+1} = au_{2} + b \iff u_3 = au_{2} + b

    But from the first part of the question, you know that u_3 = 3^{3} - 2= 27 - 2= 25 and u_2 = 7

    So: u_3 = au_2 + b\iff 25 = 7a + b
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    (Original post by Zacken)
    So, when you plugged n=1 in, you got: (i.e: wherever you see n, you put a 1)

    u_{1+1} = au_{1} + b \iff 7 = a + b

    Now, when you plug n=2 in you get: (i.e: wherever you see n, you put a 2)

    u_{2+1} = au_{2} + b \iff u_3 = au_{2} + b

    But from the first part of the question, you know that u_3 = 3^{3} - 2= 27 - 2= 25 and u_2 = 7

    So: u_3 = au_2 + b\iff 25 = 7a + b


    Well - thats a bit of a tricky one...

    Basically what I did was

    U2 = a +b = 7 from the first bit

    Then for u3

    u3 = au2 +b

    u3 = a(a+b-7) +b

    :-/
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    (Original post by christinajane)
    Well - thats a bit of a tricky one...

    Basically what I did was

    U2 = a +b = 7 from the first bit

    Then for u3

    u3 = au2 +b

    u3 = a(a+b-7) +b

    :-/
    Well, that's valid - but, doesn't really help at all so there's no point doing it. I guess it'll come with practice; do note that Solomon papers are rather different to the actual exam, so don't be put off.
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    Yeah paper E is the hardest one so far!!!

    At least what I did is kinda valid - its what I do for the other questions of this type - but obviously it wouldnt have worked out.

    I just knew I had to get a simultaneous equation - two linear ones not one linear and a quadratic!


    Solomons are very tricky - its tiny little details that keep catching me out - like the other one I just posted. I figured it out but it messed up the next bit of the question.

    I got x = 60 but coz its - x in the equation that actually means its -60! Which I didnt realise and messed the thing up - was only out by two though.

    Again my methods are there - just wrong numbers and signs :-/

    Hopefully the proper exam wont be AS tricky
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    (Original post by christinajane)
    Yeah paper E is the hardest one so far!!!

    At least what I did is kinda valid - its what I do for the other questions of this type - but obviously it wouldnt have worked out.

    I just knew I had to get a simultaneous equation - two linear ones not one linear and a quadratic!
    It's okay if you had a quadratic one, the only problem is that you get a(7a + b) + b but it's not equal to anything you know, so it's a bit useless in that sense.
 
 
 
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