Chapter 12 - Sequences; Induction; the Binomial Theorem - 12.2 Arithmetic Sequences - 12.2 Assess Your Understanding - Page 814: 17

$a_n=3n-1$ $a_{51}=152$

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 $a_n=2+(n-1)3\\ a_n=2+3n-3\\ a_n=3n-1$ Therefore, $a_{51}=3\cdot51-1\\ a_{51}=153-1\\ a_{51}=152$