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2000 paper 1 Q5 sequences

kimmy72889

Posted 03 April 2005 - 07:53 PM

has anyone done q5 from 2000's paper 1?

Two sequences are generated by the reccurence relations U(n+1)=aUn + 10 and U(n+1)=a^2Un + 16.
The two sequences approach the same limit as n --> infinity
Determine the value of a and evaluate the limit.

it would be great if someone could help! smile.gif

Dave

Posted 03 April 2005 - 08:04 PM

if the limit is the same it means that at U infinity.gif is that same in both equations

this means we can equate both equations as below

aU + 10 = a2U + 16
aU = a2U + 6
aU/a2U = 6

1/a = 6
a = 1/6

now the limit is easy

L= b/1-a

L= 10 / 1-1/6

L = 12


kimmy72889

Posted 03 April 2005 - 08:27 PM

but the answer says

a=3/5 L=25 huh.gif

Dave

Posted 03 April 2005 - 08:40 PM

sorry got it now


i had the wrong logic

if the limit is the same then you eqaute the limit equation for both sequences

so you get

10/1-a = 16/1-a2

10/16 = 1-a/1-a2

5/8 = 1/1-a

8/5 = 1-a

a = 3/5

L = 10/1-3/5 = 25

kimmy72889

Posted 03 April 2005 - 08:44 PM

why are you so good at maths?!?!?!?! mad.gif
and are you still young?

Dave

Posted 03 April 2005 - 08:46 PM

still young???

eh well i am 18...youngish then i guess!

i am doing advanced higher so i have already done all this before and now doing it again but in more depth so you get quite good at this when you do it to death

kimmy72889

Posted 03 April 2005 - 08:54 PM

oh right! god i thought you were like 40 or something (dunno why now) take it you got an A in the exam? got any tips? smile.gif

Dave

Posted 03 April 2005 - 08:55 PM

yeah i got an A <insert cheeky grin>

Tips.............

Do tons of examples and make sure you know how to do every single question in your past papers basically thats all i did

Ally

Posted 03 April 2005 - 09:17 PM

QUOTE(kimmy72889 @ Apr 3 2005, 09:54 PM)
oh right! god i thought you were like 40 or something (dunno why now)

View Post


laugh.gif LOL.

That was quite funny.

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