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**rainbow x****Member**- Registered: 2007-02-27
- Posts: 3

if anyone could help me with this, it would be very much appreciated, thankyou!

how do i work out the nth term in the following sequence? could someone explain it to me please.

11, 44, 110, 220 <--SEQUENCE

..+33 +66 +110 <-- 1st DIFFERENCE

....+33 +44 <-- 2nd DIFFERENCE

.......+11 <-- 3rd DIFFERENCE (constant)

im stuck cos ive learnt that to work out the nth term for quadratic sequences, the second difference has to be a constant, but here, the third difference is a constant .

does that make sense?

thnks for any help =]

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**Toast****Real Member**- Registered: 2006-10-08
- Posts: 1,321

I'm pretty sure it must be a cubic, can't think of any thing else... at the moment.

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**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

Yes, its cubic. Ive just worked it out.

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**rainbow x****Member**- Registered: 2007-02-27
- Posts: 3

mhmm, makes sense that it would be cubic, im still not too sure how to go about working it out though =S

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**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

Well, you just let

Since you know the values of *x[sub]n[/sub]* for *n*=1,2,3,4, substitute these into the equation and you can work out the coefficients *A*. *B*. *C*. *D*.

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

Jane is correct. It might get a bit ugly, as you have 4 simultaneous equations with 4 unknowns, but that's the way to get the answer.

There is an alternative way of getting it by using differences, but I'm not sure whether or not it would be more efficient. As you've already found the 3rd difference to be a constant of 11 though, you might as well use that to start you off.

The difference is on the **3rd** row, which means that the x³ coefficient (A, in Jane's notation) is 11/**3!** = 11/6.

From there, there are two ways of going forward.

1) Find B, C and D using the 4 simultaneous equations.

2) Keep using differences. Take away 11/6x³ from all the terms to get a new sequence which should have a common 2nd difference, which you use to find B (Divide the constant by 2!). Then take away Bx² from them all to get a new sequence with a common difference (that is also C), then use that to find the constant D.

I'm not sure which of those two is quicker (probably the first, actually), but they both definitely work.

Why did the vector cross the road?

It wanted to be normal.

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**numen****Member**- Registered: 2006-05-03
- Posts: 115

10+1, 40+4, 100+10, 200+20

Skip the second terms for a while and let us simplify the sequence: 1, 4, 10, 20

It's much easier now! We get: n/6(n+1)(n+2)

But that was the simplified model, let's continue:

--> 5n/3(n+1)(n+2) corresponds to the sequence 10,40,100,200. Now we need to add 1/10 of these:

5n/3(n+1)(n+2)+5n/30(n+1)(n+2) =

= 10n/6(n+1)(n+2)+1n/6(n+1)(n+2) =

= 11n/6(n+1)(n+2)

Inserting n=1,2,3,4 you'll see it works out fine for your sequence

Bang postponed. Not big enough. Reboot.

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