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

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    -2, 0, 4, 10, 18

    *please can you also give me an explanation
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    (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.
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    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  n^2 +an+b because we half the 2 to get the coefficient of the  n^2 term. Do you what you can do from here?
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    (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 n^2 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.
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    (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  n^2 +an+b because we half the 2 to get the coefficient of the  n^2 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?
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    (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 n^2 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...
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    (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  n^2 , then subtract the  n^2 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  n^2 which will give you the nth term in the form  n^2+an+b as required.
 
 
 
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