Question

14
С.
if for a G.P S2= 8 and S4=80
find its first team and the common ratio​

Answer 1

Answer:

First term is a, S2=a+ar=8, S4=a+ar+ar^2+ar^3=80 where a is the first term and r the ratio of consecutive terms. So a(1+r)=8 and a=8/(1+r); a(1+r+r^2+r^3)=80; 8(1+r+r^2+r^3)/(1+r)=80; 1+r+r^2+r^3=10+10r; r^3+r^2-9r-9=0; r(r^2-9)+r^2-9=0; (r^2-9)(r+1)=0; (r-3)(r+3)(r+1)=0, so r=±3, -1

mark as Braillist