There are n A.M's betwee earen A.M'...
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There are n A.M's betwee earen A.M's between 3 and 54 such that the 8th mean: (n - 2)th mean:: 3:5. The value of n is. (A) 12 (B) 16 (C) 18 (D) 20 HD

JEE/Engineering Exams
Maths
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[ begin{array}{c} frac{3+8 d}{3+(n-2) d}=frac{3}{5} 9+3 n d-6 d=15+400 3 n d=46 d+6(0) n d=frac{46}{3} d+2 quad-(1) end{array} ] If there are ( n ) A.M b/w sand 54 , then ( (n+2) ) terme are there in [ A cdot P ] hence, ( t_{n+2}=3+(n+1) d=54 ) ( (a)(n+1) d=n d+d=51-(2) ) By sut nd flom (1) in (2) we get ( d=3 ) [ therefore n=16 ]
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