The equation for missing order in the double-slit diffraction pattern→
The nature of the diffraction pattern due to the double slits depends upon the relative values of $e$ and $d$. If, however, $e$ is kept constant and $d$ is varied, then certain orders of interference maxima will be missing.

We know that, the direction of interference maxima

$(e+d)\:sin\theta=\pm n\lambda \qquad(1)$

The direction of diffraction minima

$e \: sin\theta=\pm m\lambda \qquad(2)$

Divide the equation $(1)$ by equation $(2)$

$\frac{(e+d)}{e}=\frac{n}{m}$

Case (I)→

If $e=d$ then

n=2m

So for $m=1,2,3,....$

The $n=2,4,6,....$

Thus, the $2_{nd}, 4^{th}, 6^{th}, ...$ order interference maxima will be missing.

Case (II) →

If $e=\frac{d}{2}$ then

n=3m

So for $m=1,2,3,....$

The $n=3,6,9,....$

Thus, the $3_{rd}, 6^{th}, 9^{th}, ...$ order interference maxima will be missing.