Formulae for destructive interference There are two formulae for destructive interference. In which situation do we use them? 
$$(n+1/2)\lambda $$
and 
$$(n-1/2)\lambda $$
I'm confused as my book has mentioned the first one but In question both of them are used. 
 A: Destructive interference happens when the crests of one wave align with the troughs of another wave, the amplitude of the resulting wave will then be the absolute difference of the amplitudes of the source waves.
Over the span of every wavelength there is one crest and one trough, separated by half a  wavelength. So to align crests with troughs, you have to shift one of the waves by half a wavelength. It doesn't matter in which direction you do this, because waves are periodic, nothing changes when you shift a wave by one wavelength. I don't exactly know what your formulas represent, but if they are the difference in path length necessary for two initially coherent waves to destructively interfere, you can see that the difference is exactly one wavelength
$$ \left(n + \frac{1}{2} \right) \lambda - \left(n  -\frac{1}{2}\right) \lambda = 1 \lambda $$
A: Why it doesn't matter which you use
In both those formulas $n$ nominally represents any integer value so the $n \pm \frac{1}{2}$ (both of them) represent all the places half-way between the integers. They both describe the same set of values.
They are the same.
Why it could matter in class
If a question were too ask you for the path difference of "the second dark fringe" or something similar then you might expect to substitute 2 in for $n$, but then there is an ambiguity: you have to know which fringe is "first" to know how to proceed.
Here you are concerned about how you label the members of the set. 
For this reason I prefer to use things like "the dark fringe between the second and third bright fringes" when I am writing questions. Because we usually use just one formula ($n\lambda$) for numbering the bright fringes.
