How many terms are in the arithmetic sequence 6, 2, −2, …, −102? hint: an = a1 + d(n − 1), where a1 is the first term and d is the common difference 27 28 29 30

The number of sequence in the arithmetic sequence given by:
 6, 2, −2, …, −102
will evaluated as follows:
the explicit formula is:
an=a1+d(n-1)
a1=first term
d=common difference
n=number of terms
thus from the question:
a1=6
d=2-6=-4
an=-102
plugging the values in the expression we get:
-102=6-4(n-1)
solving for n we shall have:
-102-6=-4(n-1)
-108=-4(n-1)
27=n-1
thus
n=27+1
n=28

28 terms