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# math sequences watch

1. 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
2. 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.
3. 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.
4. 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.
5. 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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