Answer:
Hence geometric sequence is {5,10,20,40,80} or,{5,-10,20,-40,80}
Step-by-step explanation:
Let a₁,a₂,a₃ be the required geometric mean.
Then,5, a₁,a₂,a₃,80 are in G.P.
a= 5
Let common ratio = r
Here 80 is the 5th term.
[tex]T_n= ar^{n-1}[/tex]
[tex]T_5= a.r^{5-1}[/tex]
[tex]\Leftrightarrow 80 = 5 .r^4[/tex]
[tex]\Leftrightarrow r^4= 16[/tex]
[tex]\Leftrightarrow r=\pm2[/tex]
When r=2 when r=-2
a₁= 5.2 =10 a₁=5.(-2)=-10
a₂=5.2²=20 a₂=5.(-2)²=20
a₃=5.2³=40 a₃=5.(-2)³=-40
Hence geometric sequence is {5,10,20,40,80} or,{5,-10,20,-40,80}
