Explain the variation of valence in the periodic table

Variation of valence in a group as well as across a period in the periodic table occurs as follows :
(i) In a group : All elements in a group show the
same valency. For example, all alkali metals
(group 1) show a valency of 1+. Alkaline
earth metals (group 2) show a valency of 2+.
However the heavier elements of p-block elements (except noble gases) show two valence :
one equal to the number of valence electrons or 8- No of valence electrons and the other two less. For example, thallium (TI) belongs to group 13. It show valence of 3+ and 1+. Lead (Pb) belongs to group 14. It shows valance of 4 + and 2 +. Antimony (Sb) and Bismuth (Bi) belong to group 15. They show valence of 5 + and 3 + being more stable.
This happens due to the non-participation of the two s-electron present in the valence shell of these elements. This non-participation of one pair of s-electrons in bonding is called inert-pair effect.
(ii) In a period : The number of the valence electrons increases in going from left to right in a period of the periodic table. Therefore the valency of the elements in a period first increases, and then decreases