Chapter 12 - Sequences and Series - 12.1 Geometric Sequences - 12.1 Exercises - Page 612: 19

$${\text{the sequence is not geometric }}$$

$$\eqalign{ & {a_1} = 4,{a_2} = 8,{a_3} = - 16,{a_4} = 32,{a_5} = 64,{a_6} = - 128,... \cr & {\text{to verify that the sequence is geometric}}{\text{, divide each term except the first by }} \cr & {\text{the preceding term}} \cr & \frac{{{a_6}}}{{{a_5}}} = \frac{{ - 128}}{{64}} = - 2 \cr & \frac{{{a_5}}}{{{a_4}}} = \frac{{64}}{{32}} = 2 \cr & {\text{the ratio is not constant}}{\text{, so}} \cr & {\text{the sequence is not geometric }} \cr} $$