Question

Find the 8th term of the geometric sequence: 1, -2, 4, -8, ...

Answer 1

$a_1=1;\ a_2=-2\\\\r=a_2:a_1\to r=-2:1=-2\\\\a_n=a_1r^{n-1}\to a_n=1\cdot(-2)^{n-1}=(-2)^{n-1}\\\\a_8=(-2)^{8-1}=(-2)^7=-128\\\\Answer:\boxed{a_8=-128}$