Q) Let $V(F)$ be the vector space of all arithmetic sequences over the field $F$ (real). i.e. all sequences of the form ${a, a+d, a+2d, ...}$ Then prove or disprove that $V(F)$ is isomorphic to $F^2$.
My first intuition says the answer is YES, dim($V(F)$) = 2 as it has two variable parameters $a$ and $d$, and dim($F^2$) = 2, so $V(F)$ is isomorphic to $F^2$.
But considering a general term of an AP(Arithmetic Progression) is written as $a_n=a+(n-1)d$, which gives 3 variable parameters $a,d,n$, therefore making dim(V(S))=3 and the result NO.
In this entire discussion one thing which I am extremely confused with is how to represent the basis of V(F).
Please suggest where I'm wrong and the representation of basis vectors of V(F).
Thanks in advance.