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Solomon E paper question 4

1. 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
2. (Original post by christinajane)
...
So, when you plugged n=1 in, you got: (i.e: wherever you see n, you put a 1)

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

But from the first part of the question, you know that and

So:
3. (Original post by Zacken)
So, when you plugged n=1 in, you got: (i.e: wherever you see n, you put a 1)

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

But from the first part of the question, you know that and

So:

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

:-/
4. (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.
5. 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
6. (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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