Question

determine if the sequence is geometric or arithmetic and find the ratio or difference. -1, 6, -36, 216

Answer 1

The sequence is an geometric progression;
Nth=a₁r^(n-1)
a₁ is the first term=-1
r=ratio=a₂/a₁=6/-1=-6

Nth=-1(-6^(n-1)

NTh=an

a₁=-1(-6⁰)=-1
a₂=-1(-6¹)=6
a₃=-1(-6²)=-36
a₄=-1(-6³)=216

therefore this serie is rising at an increasing fast speed, it is an geometric progression.