Five numbers are in A.P whose sum is 25 and product is 2520 if one of these five numbers is $\text{-}\frac{1}{2}$  then the greatest number amongst them is 

$\text{ Let the five terms }\mathrm{a}-2\mathrm{d},\mathrm{a}-\mathrm{d},\mathrm{a},\mathrm{a}+\mathrm{d},\mathrm{a}+2\mathrm{d}$

$\mathrm{SUM}=5\mathrm{a}=25\to \mathrm{a}=5$

$\text{ PRODUCT }=\left(25-4{\mathrm{d}}^2\right)\left(25-{\mathrm{d}}^2\right)=504$

$\begin{array}{l}\to \mathrm{d}=\pm 1,\mathrm{d}=\pm \frac{11}{2}\\ \text{ If }\mathrm{d}=\pm 1\text{ does not give }-\frac{1}{2}\text{ as a term }\end{array}$

$\therefore \text{d}=\frac{11}{2}$

$\text{ Largest term is }5+2\mathrm{d}=5+11=16$