I have a question about the negative binomial process.

It is given that  \left(X_{k}\right)_{k=1,2,3,.....} is a sequence of geometric random variables
And  S_{k}=X_{1}+.....+X_{k} is negative binomial (i,p)
So  \   P\left(S_{i}=k\right) a negative binomial distribution (i,p)

Now I have to show that

 P\left(S_{i}\leq k , S_{i+1}=k+n\right) =
P\left(S_{i+1}=k+1\right) \left(1-p\right)^{n-1}

But I don't know well how to work out the joint distribution

Plz Help