A geometric sequence is repeated multiplication. A negative ratio makes successive terms alternate sides of zero.
WHAT HAPPENS IF…Find a ratio that alternates while approaching zero.
Interactive exploration
Preparing your experiment…
Connect the picture to the ideaan=rn,n=0,1,2,…
Each term is r times the previous term. When |r| < 1, magnitudes shrink toward zero. When r = −1 the terms alternate forever; when r = 1 they stay constant.
A detail that matters
Alternating signs alone do not guarantee convergence.