Question

Insert six A.M.s between` 15 and -15`

Answer 1

Let the required arithmetic means (A.M.s)between `15 and -15`

be` A_1,A_2,A_3,A_4,A_5 and A_6`

`⇒ 15,A_1,A_2,A_3,A_4,A_5,A_6 and 15   "are in" A.P`

`⇒ 15="first term"`

`⇒-15=8^(th) "term of this A.P"`

`⇒-15=15+7d`

`⇒7d=-30`

`⇒d=-30/7`

`⇒ A_1=15+d=15-30/7=(105-30)/7=75/7`

`⇒A_2=15+2d=15-60/7=(105-60)/7=45/7`

`⇒A_3=15+3d=15-90/7=(105-90)/7=15/7`

`⇒A_4=15+4d=15-120/7=(105-120)/7=-15/7`

`⇒A_5=15+5d=15-150/7=(105-150)/7=-45/7`

`⇒A_6=15+6d=15-180/7=(105-180)/7=-75/7`

Hence, required A.M.s between 15 and `-15=75/7,45/7,15/7,(-15)/7,(-45)/7 and -75/7`