<p>Our goal in this paper is to give several new <i>A</i>-operator semi-norm and <i>A</i>-numerical radius inequalities for sums of operators in a semi-Hilbert space. These inequalities improve some earlier related inequalities. In particular, some refinements of the triangle inequality are obtained, and bounds for the <i>A</i>-operator semi-norm and the <i>A</i>-numerical radius for sums of multiple operators are obtained.</p>