1:3*x^(n-1)=48;3*x^(2n-3-1)=192 =>x^(n-3)=4;x^(n-1)=16 =>x^2=4=>x=2 or x=-2 =>3*2^(n-1)=48 or 3*(-2)^(n-1)=48 =>n=5 2:a1+a4=a1+a1*x^3=a1(1+x^3)=18;a2+a3=a1(x+x^2)=12 =>(x+x^3)/(x+x^2)=18/12=3/2 =>(1+x)x/(1+x)(1-x+x^2)=3/2 =>1+x=0 or x/(1-x+x^2)=3/2 =>x=-1 or x=2 or x=1/2 =>x is integer=>x=-1 or x=2 =>if x=-1 then a1(1+(-1)^3)=18=>It is wrong. =>if x=2 then a1(1+2^3)=18=>a1=2 =>a1+a2+...+a8=2*(1-2^8)/(1-2)=510 3:Sn=a1*(1-x^n)/(1-x)=>93=a1*(2^n-1);an=48=>a1*2^(n-1)=48 =>a1*x^n=96=>a1=96/2^n =>93=96*(2^n-1)/2^n=96-96/2^n =>96/2^n=3=>2^n=32=>n=5