Final answer:
The type of inversion that includes the centromere is known as a pericentric inversion. This alteration can result in changes in the lengths of the chromosome arms and potentially affect gene orientation and expression.
Step-by-step explanation:
When the inversion does include the centromere, it is called a pericentric inversion. Pericentric inversions lead to changes in the relative lengths of the chromosome arms, which can make these inversions easily identifiable.
This type of inversion has the potential to alter gene orientation and can have effects on an organism's phenotype if it disrupts gene sequences or regulatory elements. In contrast to pericentric inversions, paracentric inversions occur outside of the centromere and do not involve changes to the arms' lengths.