# Chapter 9 - Conic Sections, Sequences, and Series - 9.3 Arithmetic Sequences - 9.3 Exercises - Page 727: 18

$n=33$

#### Work Step by Step

$a_n=-5n^2+40$ when $a_n=-5405$ $-5n^2+40=-5405$ $\implies -5n^2=-5445$ $\implies n^2=1089$ $\implies n=\sqrt{1089}=33$

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