We are given the sequence $( u _ { n } )$ defined by: $u _ { 0 } = 0$ and for every natural integer $n$, $u _ { n + 1 } = \frac { 1 } { 2 } u _ { n } + 1$. The sequence $\left( v _ { n } \right)$, defined for every natural integer $n$ by $v _ { n } = u _ { n } - 2$, is: a. arithmetic with common difference $- 2$; b. geometric with common ratio $- 2$; c. arithmetic with common difference $1$; d. geometric with common ratio $\frac { 1 } { 2 }$.