SOLUTION: Between 2 numbers whose sum is 13/6,an even number of arithmetic mean's are inserted,the sum of these numbers exceeds their number by unity,how many means are there?

Question 51322: Between 2 numbers whose sum is 13/6,an even number of arithmetic mean's are inserted,the sum of these numbers exceeds their number by unity,how many means are there?
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
Between 2 numbers whose sum is 13/6,an even number of arithmetic mean's are inserted,the sum of these numbers exceeds their number by unity,how many means are there?
let the numbers be A AND 13/6-A=(13-6A)/6
LET 2N MEANS BE INSERTED
SUM OF THE 2N+2 TERMS =(NUMBER OF TERMS/2)(FIRST TERM+LAST TERM)=
{(2N+2)/2}{13/6}=13(N+1)/6
SUM OF 2N MEANS = SUM OF 2N+2 TERMS - SUM OF FIRST & LAST TERMS =
= 13(N+1)/6 - 13/6 = 13N/6
THIS IS MORE THAN THEIR NUMBER 2N BY 1 = 2N+1
13N/6 = 2N+1
13N=12N+6
N=6

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