Chapter 5 - Number Theory and the Real Number System - 5.7 Arithmetic and Geometric Sequences - Exercise Set 5.7 - Page 329: 55

The first six terms are: $10, -40, 160, -640, 2560, -10240$.

In a geometric sequence, the next term can be found by multiplying the common ratio $r$ to the previous term. Thus, with $a_1=10$ and $r=-4$, the first six terms are: $a_1=10\\ a_2=10(-4)=-40\\ a_3=-40(-4)=160\\ a_4=160(-4)=-640\\ a_5=-640(-4)=2560\\ a_6=2560(-4)=-10240$