## 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!

### Dave

Posted 03 April 2005 - 08:04 PM

if the limit is the same it means that at U 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

a=3/5 L=25

### Dave

Posted 03 April 2005 - 08:40 PM

sorry got it now

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?!?!?!?!
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?

### 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)

LOL.

That was quite funny.