Final answer:
The 9th term of the arithmetic sequence -21, -28, -35, -42, ... is found using the formula for an arithmetic sequence and is calculated to be -77, which does not match any of the provided answer choices.
Step-by-step explanation:
To find the 9th term of the arithmetic sequence -21, -28, -35, -42, ..., we first need to determine the common difference between the terms. The common difference (d) is the difference between two successive terms, which in this case is:
-28 - (-21) = -7
Now that we know the common difference, 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, and d is the common difference. For the 9th term (a9):
a9 = -21 + (9-1)(-7)
a9 = -21 + 8(-7)
a9 = -21 - 56
a9 = -77
Therefore, the 9th term of the sequence is -77, which is not listed among the options provided. It appears there may be an error in the question or the answer choices.