Find three arithmetic means between 6 and -6

Answer

3,0,-3

Explanation

Let the required AM be ` x_(1),x_(2),x_(3)`. Then
`6,x_(1),x_(2),x_(3),-6` are in AP.
Now,` T_(5)=-6 Rightarrow a+4ed =-4 Rightarrow 4d=-6 Rightarrow 4d =-12 Rightarrow d=-3`
`x_(1)=-6+d=( 6-3) =3,x_(2) =6+2d = (6-6) =0,x_(3)=6+3d =(6+3d)=(6-9) =-3`