The Goldich series does not contain rocks such as basalt. It contains the minerals that make up the rocks, generally igneous rocks such as basalt. Thus we have to be somewhat general, but we should expect to see basalt in the upper range of the Goldich series.
As with most rocks, the mixture of minerals includes both continuous and discontinuous components in the series.
Felsic vs mafic
Igneous rocks commonly found at the surface are classified as felsic or mafic, which correlates with their silica content: felsic is higher silica an mafic is lower silica. The latter corresponds to minerals that are higher on the Goldich series, such as pyroxenes.
The big reveal: basalt is mafic
So basalt, being a rock, does not have its own entry in the Goldich series, but it is the classic example of a mafic rock. Therefore relatively low silica, and high on the Goldich series. A typical weight-percent composition is given by Shrivasta et al. 1:
The silica level is similar to that in pyroxenes and in calcium-rich plagioclase feldspar (which are themselves major component minerals in basalt), so we should expect basalt to appear in the upper range of the Goldich series. Since basalt contains both pyroxenes and feldspar, it has both discontinuous and continuous components.
- Shrivastava, J. & Rani, Nishi & Pathak, Vamdev. (2016). "Geochemical Modeling and Experimental Studies on Mineral Carbonation of Primary Silicates for Long-term Immobilization of CO 2 in Basalt from the Eastern Deccan Volcanic Province." Journal Indian Geophysical Union. Special volume -1. 42-58.