Question

Between two numbers whose sum is $\frac{13}{6}$ an even number of A.M.s are inserted, the sum of these means exceeds their number by unity. Find the number of means.

Answer 1

Let a and b be two numbers and 2n A.M.s are inserted between a and b then
$\frac{2n}{2}(a+b)=2n+1$
$\Rightarrow n\left(\frac{13}{6}\right)=2n+1$
$[Givena+b=\frac{13}{6}]$
$\Rightarrow n=6$
$\therefore$ Number of means = 12