There are n AM's between 3 and 54.Such that the 8th mean and `(n-2)`th mean is 3 ratio 5. Find n.

Explanation

Let `A_(1),A_(2),A_(3),"…..",A_(n)` be n AM's between 3 and 54.
If d be the cmmon differenc, than
`d=(54-3)/(n+1)=(51)/(n+1) " ' "……(i)"`
Acccording to the example, `(A_(8))/(A_(n-2))=(3)/(5)`
` implies 5(3+8d)=3[3+(n-2)d] implies 6=d(3n-46)`
` implies 6=(3n-46)(51)/((n+1)) " " [" from Eq. (i) "]`
` implies 6n+6=153n-2346 implies 147n =2352`
`therefore " " n=16`