1. slope of L1 = -[(2k+1)/3] * slope of L2 = -[3/(1-3k)] ———————————– = -1 2k+1=-(1-3k) 2=k k=2 L1: 5x+3y-7=0 L2: 3x-5y-11=0 solving y=-1 x=2 pt of intersection : (2,-1) 2. let a be the first term, r be the common ratio a. S(3)=95 a(r^3-1)/(r-1)=95—–1 S(6)-S(3)=-6+2/25=-148/25 a(r^6-1)/(r-1) -95=-148/25 a(r^6-1)/(r-1)=2227/25——2 2/1 : (r^6-1)/(r^3-1)=2227/2375 2375r^6+2227r^3-148=0 r^3=1(rejected) or -148/2375 r=-0.39646 b. when r=-0.39646 a[(-0.39676)^3-1]/(-0.39646-1)=95 a=124.8816

c S(inf) =a/(1-r)=124.8816/(1-(-0.39646))=89.4273