In order to solve for a nth term in an arithmetic sequence, we use the formula written as:
an = a1 + (n-1)d
where an is the nth term, a1 is the first value in the sequence, n is the term position and d is the common difference.
First, we need to calculate for d from the given values above.
a1 = 38 and a17 = -74
an = a1 + (n-1)d
-74 = 38 + (17-1)d
d = -7
The 27th term is calculated as follows:
a27 = a1 + (n-1)d
a27= 38 + (27-1)(-7)
a27 = -144 -----------> OPTION D