## Algebra 2 (1st Edition)

$\left\{\begin{array}{l} a_{1}=19\\ a_{n}=a_{n-1}-6 \end{array}\right.$
Note the common difference between consecutive terms ($d=-6$). This is an arithmetic sequence, for which we have $a_{n}=a_{n-1}+d,$ In this case, $a_{n}=a_{n-1}-6.$ For a recursive rule, we give the information about the first term, and a rule on how to obtain the next term from the preceding: $\left\{\begin{array}{l} a_{1}=19\\ a_{n}=a_{n-1}-6 \end{array}\right.$