Sequence recurrence relationship

[mattgad]

I'm having problems with the above question.

So far, I've tried working out U2 as being 2p + 5, subbing in p = 0.5 to get U2 = 6. So then U3 is 6p + 5, which is 8, making U4, 8p + 5, = 9.

Am I doing this wrong?
Can anyone show me what I need to do to prove that p = 1/2 and what method I would use to find the other value of p.

Thanks,

 

[pka]

You have not correctly determined the terms.
\(\displaystyle {
u_1 = 2 \cr
u_2 = 2p + 5 \cr
u_3 = p(u_2 ) + 5 = 2p^2 + 5p + 5 \cr
u_3 = 2p^2 + 5p + 5 = 8 \cr}\)
Now solve that last equation.

 

[mattgad]

Thanks. That all makes sense. I then factorised the quadratic to get
(2p - 1)(p + 3), making p = 1/2 or p = -3.

Is that correct?

This question is worth 3 marks, so I'm not sure if I've done it right. All I've done is sub p = 4 into the terms. Is this really worth 3 marks?

(4), 5(4) - 8, 3(4) + 8 = 4, 12, 20

Common difference = 8.

Have I done this correctly? and do I need to state anything else to pick up full marks?

Thanks.

 

[pka]

Yes the first is correct.

Now, please post a new topic with each new question!

You are asked to PROVE something not verify it.
You need to show that if (5p−8)−(p)=(3p+8)−(5p−8) then p=4.

 

[stapel]

I then factorised the quadratic to get (2p - 1)(p + 3), making p = 1/2 or p = -3. Is that correct?

Yes.

Is this a new question? If so, please post it as a new thread, not as a reply to an old question. When you post this, there is no need to insert an image; please just type out the text, as:

The first three terms of an arithmetic series are p, 5p - 8, and 3p + 8. Show that p = 4.

This question is worth 3 marks, so I'm not sure if I've done it right.

You say that you're not sure of your answer because the question is worth three points. Why is the correctness of your answer dependent on the number of points? Please clarify.

Is this really worth 3 marks?

How would we know any different than what you've told us...?

Eliz.

 

[mattgad]

You say that you're not sure of your answer because the question is worth three points. Why is the correctness of your answer dependent on the number of points? Please clarify.

I wondered if anyone was from the UK, they may know what I mean. Usually the number of points depends on what you show, and I was wondering if I had shown 3 valid points to get me full marks.

How would we know any different than what you've told us...?

You wouldn't, I have no idea why I asked that.

 

[Unco]

<--Thread has sub-branched off to another (just so no one gets confused)-->

Re. the number of points awarded for the question: compare with similar questions from past papers; don't get too caught up with it - so long as you know or are beginning to know how to do it, you'll be sussed.