A diatomic gas with a single stable isotope will give two peaks in
the mass spectrometer. One of these peaks will be the molecular
ion. The other peak will be seen at half the m/z of the molecular
ion, and will be due to a fragment of the diatomic gas. For
example, Nitrogen gas would give a molecular ion peak due to
$N_2^+$ and a fragment peak due to $N^+$.

Look for key facts about the data: smallest numbers, largest numbers, conspicuous gaps in the sequence. What elements in individual form would give rise to some of these? From this you can probably rule out the existence of certain elements, which will allow you to make a start.

There will be an iteration of attempts as you rule out various possibilities.

Be sure to double-check that your final answer gives a convincing explanation for the whole spectrum.

Look for key facts about the data: smallest numbers, largest numbers, conspicuous gaps in the sequence. What elements in individual form would give rise to some of these? From this you can probably rule out the existence of certain elements, which will allow you to make a start.

There will be an iteration of attempts as you rule out various possibilities.

Be sure to double-check that your final answer gives a convincing explanation for the whole spectrum.