# Chapter 9 - Section 9.2 - Arithmetic Sequences - 9.2 Assess Your Understanding - Page 654: 18

$a_n=-2+4(n-1)$ $a_{51} = 198$

#### Work Step by Step

RECALL: The $n^{th}$ term of an arithmetic sequence can be found using the formula: $a_n = a_1 + (n-1)d$ where $a_1$ = first term and $d$ = common difference The given sequence has: $a_1=-2$; $d=4$ Substitute these values into the formula for the $n^{th}$ term to obtain: $a_n=a_1 + (n-1)d \\a_n=-2+(n-1)(4) \\a_n=-2+4(n-1)$ To find the 51st term, substitute $51$ for $n$ to obtain: $a_{51} = -2+4(51-1) \\a_{51}=-2+4(50) \\a_{51} = -2+200 \\a_{51} = 198$

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