Step 1: Determine the positions of X, Y, and Z in the periodic table.
The atomic numbers are consecutive: $Z_{\text{X}}=a$, $Z_{\text{Y}}=a+1$, $Z_{\text{Z}}=a+2$. This means X, Y, and Z are elements that appear one after the other in the periodic table (or X and Y are in one period and Z is in the next).
The element Z ($Z_{\text{Z}}=a+2$) is an alkali metal. Alkali metals belong to Group 1 (IA).
Step 2: Determine the group of X and Y.
If Z is in Group 1, then the element immediately preceding it in the same period is a noble gas (Group 18), or an element from the previous period (Group 17).
A noble gas (Group 18) has an atomic number $Z_{\text{NG}}$. The next element, the alkali metal (Group 1), has $Z_{\text{NG}}+1$. If $Z_{\text{Z}}$ is an alkali metal, then $Z_{\text{Z}}-1$ is a noble gas.
So, Y ($Z_{\text{Y}}=a+1$) must be a noble gas (Group 18), and X ($Z_{\text{X}}=a$) must be a halogen (Group 17).
Step 3: Analyze the nature of the elements X and Z.
Z is an alkali metal (Group 1, low ionization energy, high tendency to lose $e^-$ to form $Z^+$).
X is a halogen (Group 17, high electron affinity, high tendency to gain $e^-$ to form $X^-$).
Alkali metals are typical metals, and halogens are typical non-metals.
Step 4: Determine the nature of the bond between X and Z.
A compound formed between a metal (Z) and a non-metal (X), where there is a large difference in electronegativity, will involve the transfer of electrons and result in an electrostatic attraction between the resulting ions.
The bond formed by the electrostatic attraction between $Z^+$ and $X^-$ is an ionic bond.