Question

Insert five A.M.s between -12 and 8.

Answer 1

Let the required arithmetic means (A.M.s) between -12 and 8 be `A_1,A_2,A_3,A_4 and A_5`

`⇒ -12,A_1,A_2,A_3,A_4,A_5  "and 8 are in A.P"`

`⇒ -12=` first term 

`⇒ 8=7^(th)` term of this A.P

`⇒8=-12+6d`

`⇒6d=20`

`⇒ d=10/3`

`⇒ A_1=-12+d=-12+10/3=(-36+10)/3=-26/3`

`⇒ A_2=12+2d=-12+20/3=(-36+20)/3=-16/3`

`⇒ A_3=-12+3d=-12+30/3=(-36+30)/3=-6/3`

`⇒A_4=-12+4d=-12+40/3=-36+40/3=-4/3`

`⇒A_5=-12+5d=-12+50/3=-36+50/3=-14/3`

Hence, required A.M.s between -12 and `8=-26/3,-16/3,-6/3,-4/3 and -14/3`