If l,m,n are three numbers in G.P then the ratio of first Term to the common difference  of an A.P whose $l^{th},m^{th}and{n}^{th}$ Terms are in H.P is equal to ______________

 $a+(m-1)d=\frac{2[a+(l-1)d](a+(n-1)d)}{a+(l-1)d+a+(n-1)d}$
 $\Rightarrow ad[(2m-2+l+n-2)-(2(n-1)+2(l-1))]=d^2[2(l-1)(n-1)-(l+n-2)(m-1)]$$\Rightarrow \frac{a}{d}=\frac{2\ln -l-n-lm-mn+2m}{2m-n-l}=\frac{(2m-l-n)(m+1)}{(2m-l-n)}$
 
 = m+1