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  • Three are n AM between 3 and 54 such that 8th mean is to (n-2)th mean as 3 to 5. Find n.

Three are n AM between 3 and 54 such that 8th mean is to (n-2)th mean as 3 to 5. Find n.

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Solution:   Let   A_1 , A_2 , A_3, ...........A_n  be n AM between 3 and 54

                   If   d  be common difference , then 

                                                                d=frac54-3n+1=frac51n+1         .........(1)

                  Rightarrow                 fracA_8A_(n-2)=frac35

                 Rightarrow               5(3+8d)=3[3+(n-2)d] Rightarrow 6=(3n-46)d

                Rightarrow                 6n+6=153n-2346Rightarrow n=16.  

Posted by

Deependra Verma

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