Identify the 27th term of an arithmetic sequence where a1 = 38 and a17 = -74. a. -20.5 . b. -151 . c. -22.75 . d. -144 .

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

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