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Hi all,

I was just wondering whether one could define arithmetic sequences in R^2 in a simmilar manner as in R.?

Here is what i see as a natural way of doing it, but neither have i read about it, nor heard.

[tex] \mbox{ Let } x_n \in R^2 \mbox{ be a sequence given as follows : } x_n=a+mb\\, \mbox{ where } a,b,m\in R^2.[/tex]

[tex]\mbox{ That is, } a=(a_1,a_2),b=(b_1,b_2),m=(m_1,m_2). \mbox { So, } x_n=(a_1+m_1b_1,a_2+m_2b_2). \mbox{ We call such a sequence an arithmetic sequence in } R^2.[/tex]

Would this definition be valid? If so, i believe one could define an arithmetic or geometric sequence in R^n as well. Right?

EDIT: Or maybe on a second thought i think that the following change would be better:

[tex] x_n=(a_1+nb_1,a_2+nb_2)=(a_{1n},a_{2n}). \mbox{ That is letting } m=(m_1,m_2)=(n,n).[/tex]

Thnx

I was just wondering whether one could define arithmetic sequences in R^2 in a simmilar manner as in R.?

Here is what i see as a natural way of doing it, but neither have i read about it, nor heard.

[tex] \mbox{ Let } x_n \in R^2 \mbox{ be a sequence given as follows : } x_n=a+mb\\, \mbox{ where } a,b,m\in R^2.[/tex]

[tex]\mbox{ That is, } a=(a_1,a_2),b=(b_1,b_2),m=(m_1,m_2). \mbox { So, } x_n=(a_1+m_1b_1,a_2+m_2b_2). \mbox{ We call such a sequence an arithmetic sequence in } R^2.[/tex]

Would this definition be valid? If so, i believe one could define an arithmetic or geometric sequence in R^n as well. Right?

EDIT: Or maybe on a second thought i think that the following change would be better:

[tex] x_n=(a_1+nb_1,a_2+nb_2)=(a_{1n},a_{2n}). \mbox{ That is letting } m=(m_1,m_2)=(n,n).[/tex]

Thnx

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