The common difference between two terms(d)=46-38=38-30=8
Now if a is a term of this AP series then
a-48 must be a multiple of d=common difference
Now here ,we are given that a=-116.
We would check whether this is a term of the AP or not.
a-48=-116-46=-162
But 162 is not a multiple of 8.
Hence -116 is not in this AP