Using SUMPRODUCT
Here's another formula you can use, which is a slightly better choice:
=SUMPRODUCT((MOD(ROW($A$1:$A$10),2)=0)*($A$1:$A$10))
You should, however, be aware that this formula will return #VALUE! if any cells in the range contain text rather than numbers. This formula, although not a true array, also will slow down Excel if too many instances of it are used, or if those instances reference a large range.
Fortunately, there is a much better way that is not only more efficient, but also far more flexible.