Chapter 12 - Sequences; Induction; the Binomial Theorem - 12.2 Arithmetic Sequences - 12.2 Assess Your Understanding - Page 814: 19

$a_n=-3n+8.$ $a_{51}=-145.$

We know that the $n^{th}$ term $a_n$ of an arithmetic sequence is given by the formula $a_n=a_1+(n-1)d$ where $d$=common difference and $a_1$= the first term Hence, here we have $a_n=5+(n-1)\cdot(-3)\\a_n=5-3n+3\\a_n=-3n+8.$ Therefore $a_{51}=-3\cdot51+8\\a_{51}=-153+8\\a_{51}=-145.$