Which of the following recurrence relation correctly describes the given scenario?

$a_1=5$ and $a_n=a_{n-1}-1$ for all $n>1.$

$a_1=5$ and $a_n=2(a_{n-1}-1)$ for all $n>1.$

$a_1=5$ and $a_n=2a_{n-1}-1$ for all $n>1.$

$a_1=5$ and $a_n=1-a_{n-1}$ for all $n>1.$