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

Answer: 28 terms