The increasing order of reactivity among group $1$ elements is $Li < Na < K < Rb < Cs$ whereas that among group $17$ elements is $F > Cl > Br > I$. Explain.

(N/A) The elements in group $1$ have $1$ valence electron,which they lose to form cations. As we move down the group,the ionization enthalpy decreases,making it easier to lose the electron. Thus,reactivity increases down the group: $Li < Na < K < Rb < Cs$.
In group $17$,elements need $1$ electron to achieve a noble gas configuration. Reactivity depends on the tendency to gain electrons,which is related to electron gain enthalpy. Generally,this tendency decreases down the group. Although $F$ has a less negative electron gain enthalpy than $Cl$,it is the most reactive due to its very low bond dissociation energy. Thus,the reactivity order is $F > Cl > Br > I$.