Question

Insert four A.M.s between 14 and -1.

Answer 1

Let the required arithmetic means (A.M.s) between `14 and -1` 'be `A_1,A_2,A_3 and A_4`

`⇒ 14,A_1,A_2,A_3,A_4 and -1 are in A.P`

`⇒14= "first term" `

`⇒-1=6^"th term of this A.P"`

`⇒-1=14+5d`

`⇒ 5d=-15`

`⇒ d=-3`

`⇒ A_1=14+d=14+(-3)=11`

`⇒A_2=14+2d=14+2(-3)=-8`

`⇒A_3=14+3d=14+3(-3)=5`

`⇒A_4=14+4d=14+4(-3)=2`

Hence, required A.M.s between `14 and -1=11,8,5 and 2`