The condition that the roots of $x^3-b x^2+c x-d=0$ are in arithmetic progression is

In the expansion of $\frac{2 x+1}{(1+x)(1-2 x)}$ the sum of the coefficients of the first 5 odd powers of $x$ is

$\frac{1}{1 \cdot 5}+\frac{1}{5 \cdot 9}+\frac{1}{9 \cdot 13}+\ldots$. upto $n$ terms $=$

If the roots of the equation $4 x^3-12 x^2+11 x+m=0$ are in arithmetic progression, then $m=$