common ratio: -2/3 but since the nth term is positive i.e (512/729), this means that the power of the ratio will be an even number… .therefore.. we have to assume the -ve sign at this point since it will have no effect. hence the solution is; 512/729=18(2/3)^n-1 divide by 18 on both sides ; 256/6561=(2/3)^n-1 ; log 0.03902=(n-1) log 0.6667; log 0.03902/ log 0.6667=n-1; n-1=8; n=9;