Question

tween the two numbers whose sum is 13, an 35. Between the an 6 even number arithmetic me then number of umber of A.M is inserted. If the sum of metic mean exceeds their number by unity, number of arithmetic means inserted are - (a) 6 (b) 10 (C) 8 (d) 12

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Solution

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( Rightarrow ) let the numbers be ( A ) AND ( 13 / 6-A=(13-6 A) / 6 ) - LET 2N MEANS BE INSERTED - SUM OF THE 2N+2 TERMS =(NUMBER OF TERMS/2)(FIRST TERM+LAST TERM)= ( {(2 N+2) / 2}{13 / 6}=13(N+1) / 6 ) ( rightarrow ) SUM OF 2N MEANS = SUM OF 2N+2 TERMS - SUM OF FIRST & LAST TERMS ( =13(mathrm{N}+1) / 6-13 / 6=13 mathrm{N} / 6 ) - ( mathrm{THIS} ) IS MORE THAN THEIR NUMBER ( 2 mathrm{N} ) BY ( 1=2 mathrm{N}+1 ) ( Rightarrow 13 mathrm{N} / 6=2 mathrm{N}+1 ) ( Rightarrow 13 mathrm{N}=12 mathrm{N}+6 ) ( Rightarrow N=6 )