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# Series and Sequences C1 Help. watch

1. Well, i was given a question and i havent got a clue how to do, so i was wondering whether anyone could work out the answer and more importantly show how you did it. the question is:

The sequence U1, U2...,Un is defined by the recurrence relation:
Un+1=pUn+5, U1=2, where p is a constant.
Given that U3=8
Show that one possible value of p is 1/2 and find the other value of p.
Thanks
2. anyone?
3. seem everyone seems to be sour I'll try help you out m8. I'm doing C1 aswell so I might not be pro but I'll give it a go for good practice.

This is what I'd do.

Basically this is to prove p is 0.5

Un+1 = pUn+5
sub in 2 cause you know its 1st term

2=pUn+5
sub in p cause you know its 0.5

2=0.5Un+5

solving it will give the Un as -6

Do it for the second term aswell and check and then do it for third term and it will equal 8 which is what it says.

ermmm now finding the other value for p I don't relly get that bit unless its something to do with quadratics :
4. Or maybe another value for p is -0.5 but that would mean Un is positive instead of negative. Sorry if I haven't been much help but I gave it a bash only topic that gets to me in C1 this.
5. I'm saddened that I don't know what to do
6. I don;t know if p as -0.5 is a possibility
7. Ok... Hopefully this should help:

We know that : Un+1=pUn+5 and U1=2

So therefore U2 = pU1+5
=2p+5

So therefore U3 = pU2+5
= p(2p+5) + 5
= 2p²+5p+5

And we are given U3 = 8
So therefore: 2p²+5p+5=8
2p²+5p-3=0
(2p-1)(p+3)=0

So therefore, p=0.5 (given) or p=-3
8. Ok... Hopefully this should help:

We know that : Un+1=pUn+5 and U1=2

So therefore U2 = pU1+5
=2p+5

So therefore U3 = pU2+5
= p(2p+5) + 5
= 2p²+5p+5

And we are given U3 = 8
So therefore: 2p²+5p+5=8
2p²+5p-3=0
(2p-1)(p+3)=0

So therefore, p=0.5 (given) or p=-3
9. Sorry, computer went a bit nuts. Apologies for the duplicate post.
10. (Original post by greenjm90)
Ok... Hopefully this should help:

We know that : Un+1=pUn+5 and U1=2

So therefore U2 = pU1+5
=2p+5

So therefore U3 = pU2+5
= p(2p+5) + 5
= 2p²+5p+5

And we are given U3 = 8
So therefore: 2p²+5p+5=8
2p²+5p-3=0
(2p-1)(p+3)=0

So therefore, p=0.5 (given) or p=-3
Ahhhhhh you're actually a genius...thank you soo much and thanks everyone else.

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