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    (i)The sum of the first n terms of a series is given by

    Sn = n^2 + 5n

    Find an expression for the nth term, Un.

    (ii)Prove that the series is arithmetic and write down the first four terms.

    Could some1 help me on the above question plzzz
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    (Original post by Bilal786)
    (i)The sum of the first n terms of a series is given by

    Sn = n^2 + 5n

    Find an expression for the nth term, Un.

    (ii)Prove that the series is arithmetic and write down the first four terms.

    Could some1 help me on the above question plzzz
    (i) If we know the sum to n then by logic the nth term is the sum to n minus the sum to (n-1) [IE: The new value that has been added is n].

    S(1) = 6. Hence term 1 = 6
    S(2) = 14. Hence term 2 = 14-6 = 8
    S(3) = 24. Hence term 3 = (24-14) = 10
    S(4) = 36. Hence term 4 = (36-24) = 12
    ..
    ..
    S(n) = n^2 + 5n.
    Term n = [n^2 + 5n] - [(n-1)^2 + 5(n-1)] = [n^2 + 5n] - [n^2 - 2n + 1 + 5n - 5] = [n^2 + 5n] - [n^2 + 3n -4] = 2n +4

    (ii) The nth term is given by 2n+4. Clearly the first term is 4 and the common difference is a factor of 2. It is clearly an arithmetic series. The first four terms are listed above as 6,8,10,12.
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