We carried out a first-principles quantum-mechanical study of a set of full-turn A-form DNA oligonucleotides using density functional approximations. The structural features of the fully relaxed model DNA molecules and more importantly, the energetic and structural changes of these molecules under stretching conditions are examined in detail. Special attention is paid to the dependence of the structural properties on the stacking sequences of the constituent DNA base pairs. It appears that DNA oligonucleotides are extremely flexible, and structural properties such as the diameter and the widths of the minor and major grooves change regularly as a function of the stretching rate (stretching length in percentage). Additionally, we found that the length of the hydrogen bonds in the DNA base pairs varies with the DNA stacking sequence. This work indicates that rich information and insights can be gained from first principles studies of model DNA molecules of only O(102-103) atoms.