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# How to find the formula for the nth term of this sequence:

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1. -2, 0, 4, 10, 18

*please can you also give me an explanation
2. (Original post by themortalprince)
-2, 0, 4, 10, 18

*please can you also give me an explanation
No, what have you tried? What's the differences between each term? C'mon, show some effort.
3. The sequence increases by 2 then 4 then 6 then 8. The difference of the difference between consecutive terms stays the same at 2. This is a quadratic sequence in other terms. As the common difference is 2 the nth term will be of the form because we half the 2 to get the coefficient of the term. Do you what you can do from here?
4. (Original post by themortalprince)
-2, 0, 4, 10, 18

*please can you also give me an explanation
The first differences are 2, 4, 6, 8 which is an arithmetic sequence.

Which means this must be a quadratic sequence.

I would start by looking at the simplest quadratic sequence with nth term and compare it with your sequence

1. 4. 9. 16. 25....
-2, 0, 4, 10, 18, ...

Look at the difference between the terms (e.g. 1-(-2) = 3) and see if you notice a pattern.

Post all your working/ideas if you get stuck.
5. (Original post by B_9710)
The sequence increases by 2 then 4 then 6 then 8. The difference of the difference between consecutive terms stays the same at 2. This is a quadratic sequence in other terms. As the common difference is 2 the nth term will be of the form because we half the 2 to get the coefficient of the term. Do you what you can do from here?
Thank you! Do you mind if I ask you more questions?
- This how I get stuck on this question

-2 , 0 , 4 , 10 , 18
2 4 6 8
2 2 2 --------------- ( n^2)
1 4 9 16 25
3 4 5 6 7 -------- what am I supposed to do after this?
6. (Original post by notnek)
The first differences are 2, 4, 6, 8 which is an arithmetic sequence.

Which means this must be a quadratic sequence.

I would start by looking at the simplest quadratic sequence with nth term and compare it with your sequence

1. 4. 9. 16. 25....
-2, 0, 4, 10, 18, ...

Look at the difference between the terms (e.g. 1-(-2) = 3) and see if you notice a pattern.

Post all your working/ideas if you get stuck.
I know that in the formula there is n^2 but I don't how to find the rest of the formula...
7. (Original post by themortalprince)
I know that in the formula there is n^2 but I don't how to find the rest of the formula...
Make a table of 2 rows. Make the first row your original quadratic sequence. Underneath it put the sequence , then subtract the sequence from you original, it should leave the sequence -3, -4, -5, -6 ... which is linear. Find the nth term of the linear sequence and just add that to the which will give you the nth term in the form as required.

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