Combination of different antennas
Technically, yes, the radiation pattern is the sum of the individual element radiation patterns, adjusted for geometric differences in distance to the receiving point. But you're mixing together several fundamental antenna concepts:

The size of individual antenna elements (you've suggested /2 and /4 as examples).

The arrangement of several antenna elements to create an array (orientation of, and spacing between, the elements).

The radiation pattern of the resulting array.


And you've not considered the important factor of how the individual elements are excited (i.e. fed with RF energy). When you have more than one antenna element, there is coupling between them (mutual impedance) that affects the currents flowing in them and the impedance they present to the feeding system.
Typically, a /2 length antenna is a dipole, fed at the center (but there are variations to end-feed it). And typically, a /4 length antenna is a monopole, fed at the end and working against a ground plane. It would be unusual to design an array using these different elements together.
Here are some practical examples you will see:

Simple /2 dipole antenna: old-fashioned TV &quot;rabbit ears&quot;
Simple /4 monopole against ground: AM radio station with one tower
Phased array of /4 monopoles against ground: AM radio station with multiple towers (to produce specific nulls to protect other stations from interference)
Array of /2 dipoles, with one or two elements fed, and other elements passively excited: Yagi-style outdoor TV antenna