Find 7 arithmetic means between 6 and 46.

Answer

N/a

Explanation

Let 7 arithmetic means beween 6 and 46 are `A_(1),A_(2),...,A_(7).`
`therefore" "6,A_(1),A_(2),A_(3),...,A_(7),"46 are in A.P."`
`"and "T_(9)=46`
`rArr6+(9-1)d=46`
`rArr " "8d=40`
`rArr " "d=5`
`"Now, "A_(1)=a+d=6+5=11`
`A_(2)=a+2d=6+2xx5=16`
`A_(3)=a+3d=6+3xx5=21`
`A_(4)=a+4d=6+4xx5=26`
`A_(5)=a+5d=6+5xx5=31`
`A_(6)=a+6d=6+6xx5=36`
`A_(7)=a+7d=6+7xx5=41`
`therefore` Required arithmetic means are 11,16,21,26,31,36,41.