Chapter 11 - Sequences; Induction; the Binomial Theorem - Section 11.2 Arithmetic Sequences - 11.2 Assess Your Understanding - Page 834: 15

$a_n=2+3(n-1)$ and $a_{51} =152$

The $n^{th}$ term of an arithmetic sequence is given by the formula: $a_n = a_1 + (n-1)d (1)$ where $a_1 = \ First \ Term; \\ d = \ Common \ Difference$ We have: $a_1=2 \\ d=3$ Next, we will substitute the above data into the formula (1) to obtain: $a_n=2+(3)(n-1) \implies a_n=2+3(n-1)$ In order to compute the $51st$ term, we need to plug in $51$ for $n$ into the above form to obtain: $a_{51} = 2+3(51-1) =2+150$ So, $a_{51} =152$