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C2 Sequences

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    I've got a sequences questions which I've done wrong/not sure how to do, and would be grateful for some help.

    1. The sequence u1, u2, u3, .... is defined by un = 2n^2
    a) Write down the value of u3.
    b) Express un+1 - un in terms of n, simplifying your answer.
    c) The differences between successive terms of the sequence form an arithmetic progression. For this aritmetic progression, state its first term and its common difference, and find the sum of its first 1000 terms.

    I've done a), and I got 18. I'm not sure about how I would do b), and for c) what does it mean by successive? So does it mean, u1, u2, u3, or is it alternate ones?

    Thanks
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    U_{n+1} = 2(n+1)^2

    U_n = 2n^2


    Just take the latter from the former



    Successive juts means from one to the next
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    (Original post by MedicalMayhem)
    I've got a sequences questions which I've done wrong/not sure how to do, and would be grateful for some help.

    1. The sequence u1, u2, u3, .... is defined by un = 2n^2
    a) Write down the value of u3.
    b) Express un+1 - un in terms of n, simplifying your answer.
    c) The differences between successive terms of the sequence form an arithmetic progression. For this aritmetic progression, state its first term and its common difference, and find the sum of its first 1000 terms.

    I've done a), and I got 18. I'm not sure about how I would do b), and for c) what does it mean by successive? So does it mean, u1, u2, u3, or is it alternate ones?

    Thanks
    Successive means in order, consecutive; not alternating. For b) it should be like TenOfThem said and you might have to expand the brackets but I'm not sure. For c) just find the first term and the common difference and the rest is just C1 knowledge.
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    (Original post by TenOfThem)
    U_{n+1} = 2(n+1)^2

    U_n = 2n^2


    Just take the latter from the former



    Successive juts means from one to the next
    (Original post by uttamo)
    Successive means in order, consecutive; not alternating. For b) it should be like TenOfThem said and you might have to expand the brackets but I'm not sure. For c) just find the first term and the common difference and the rest is just C1 knowledge.
    Thanks I just got a bit confused :/

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Updated: April 14, 2012
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