1. Find a real number $\displaystyle a$ such that the sequence $\displaystyle (v_n)_{n\geqslant1}$ defined by $\displaystyle v_n=u_n-a$ is geometric with common ratio $\displaystyle k$.
2. Express $\displaystyle v_n$ in terms of $\displaystyle n$ and $\displaystyle k$.
3. Express $\displaystyle u_n$ in terms of $\displaystyle n$ and $\displaystyle k$.