Chapter 11 - Sequences; Induction; the Binomial Theorem - Section 11.3 Geometric Sequences; Geometric Series - 11.3 Assess Your Understanding - Page 844: 20

The $n^{th}$ term of the sequence is given by the formula: $a_n = -2 \ (4)^{n-1}$ and $a_5= -512$

We are given: $a_{1}= -2 ; \ r= 4$ The $n^{th}$ term of the sequence is given by the formula: $a_n=a_1r^{n-1}$ $a_n = -2 \ (4)^{n-1}$ Now, the 5th term can be computed by substituting $5$ for $n$: $a_5=-2 \ (4)^{5-1} \\ =(-2)(4^4) \\=(-2) (256) \\= -512$