Chapter 12 - Sequences; Induction; the Binomial Theorem - 12.2 Arithmetic Sequences - 12.2 Assess Your Understanding - Page 814: 20

$a_n=-2n+8.$ $a_{51}=-94.$

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 $a_n=6+(n-1)\cdot(-2)\\a_n=6-2n+2\\a_n=-2n+8.$ Therefore $a_{51}=-2\cdot51+8\\a_{51}=-102+8\\a_{51}=-94.$