Final answer:
The possible arrangements of alleles on the F1 progeny's chromosomes are AaZz, aAZz, or AazZ.
Step-by-step explanation:
When genes are located in close proximity on the same chromosome, they are considered linked. In the given cross between the parents AAZZ and aazz, the F1 progeny inherits the A allele from the AAZZ parent and the a allele from the aazz parent for gene A. Similarly, for gene Z, the F1 progeny inherits the Z allele from the AAZZ parent and the z allele from the aazz parent. Consequently, the possible arrangements of alleles on the F1 progeny's chromosomes are AaZz, aAZz, or AazZ.