a) The sequence is an arithmetic sequence if and only if the following condition is true,
an - an+1 = an+1 - an ∀n >0
So, -11 - (-15) = 4 = -7 - (-11)
Hence the given sequence is an arithmetic sequence.
b) Tn = a + (n-1)d
So, the formula for the given sequence is, Tn = -15 + (n-1)*4 = 4n - 19
c) Tn = 4n - 19 where, Tn = 173
so, 173 = 4n - 19
or 192/4 = n
or n = 48
So there are a total of 48 terms