Final answer:
The common difference of the arithmetic sequence with the first term -12 and the 38th term -160 is found using the sequence's formula. After plugging in the known values and simplifying, the common difference is calculated as -4, corresponding to option A.
Step-by-step explanation:
To find the common difference in an arithmetic sequence, we can use the formula for the nth term of an arithmetic sequence, which is an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, n is the term number, and d is the common difference.
In this problem, the first term (a1) is -12 and the 38th term (a38) is -160. Plugging these values into the equation, we get:
-160 = -12 + (38 - 1)d
By simplifying the equation, we can solve for the common difference d:
-160 = -12 + 37d
-148 = 37d
d = -148 / 37
d = -4
Hence, the common difference is -4, which corresponds to option A.