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    A sequence of positive integers y1, y2,.. is given by

    y1=4 nad yn+1 = 3yn - 2

    For n_>1

    Find an expression, in terms of k, for the sum

    y1+y2+...+yk
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    dare i say it, i think more information is needed, could you state the whole question and say what level paper/book the question came from.
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    Actually, I was wondering what "in terms of" means exactly?

    P.S sorry for not posting the whole info but I thought that that was enough.
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    y in terms of x means write down y = f(x)

    say 5y = x + 5
    put y in terms of x,
    y = x/5 + 1

    so that you can find y given x without having to do any rearranging.
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    We know
    y(n+1) = 3y(n) - 2,
    y(1) = 4.

    So
    [y(n+1) - 1]
    = 3y(n) - 3
    = 3 *[y(n) - 1].

    So [y(n) - 1] triples each time you put n up by 1.

    So
    y(n) - 1
    = (y(1) - 1) * 3^(n-1)
    = 3 * 3^(n-1)
    = 3^n.

    So y(n) = 3^n + 1.

    --

    So y(1) + y(2) + ... + y(k)
    = (3 + 9 + ... + 3^k) + k
    = (1/2)[3^(k+1) - 3] + k.
 
 
 
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