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
Answer: 28 terms
