Q: Say a vector A has ten values (decision variables) Objective: Maximize the sum of A. How do I model this constraint: The sum of consecutive four elements in the vector should be less than 10.

You can use the lag and lead operator (chapter 13.4 in the GAMS User's Guide) as in the following example:

set i /1*10/; alias (i,j);
set iconseq(i,j);
scalar cnt;

loop(i, for(cnt=0 to 3, iconseq(i,i+cnt) = yes));
display iconseq;

variable x(i);
equation e(i);
e(i).. sum(iconseq(i,j), x(i)) =l= 10;

If you want your constraint to interpret “consecutive” in a circular manner, you will have to replace + in the loop-statement by ++.