Chapter 12 - Sequences; Induction; the Binomial Theorem - 12.2 Arithmetic Sequences - 12.2 Assess Your Understanding - Page 814: 18

$a_n=4n-6.$ $a_{51}=198.$

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 $a_n=-2+(n-1)4\\a_n=-2+4n-4\\a_n=4n-6.$ Therefore $a_{51}=4\cdot51-6\\a_{51}=204-6\\a_{51}=198.$