Determine whether the following sequence is arithmetic, geometric, or neither.

1 1/3, 2, 2 2/3, 3 1/3

arith

Step-by-step explanation:

Let's check whether or not this is a geometric series.

The first term is 1 1/3, or 4/3.

What would the common ratio be, to convert this 4/3 into the 2nd term, 2?

(4/3) r = 2, or r = 2 (3/4) = 6/4 = 3/2.

Assuming that the common ratio is r = 3/2, will multiplying 2 by 3/2 result in the 3rd term, 2 2/3? NO. So this is NOT a geometric progression.

The difference between 1 1/3 and 2 is 2/3. If we add 2/3 to 2, we get 2 2/3, which agrees with the given 3rd term.

If we add 2/3 to 2 2/3, do we get the fourth given term, 3 1/3?

2/3 + 2 2/3 is equivalent to 2 4/3, or 10/3, which is equivalent to 3 1/3.

Thus, this IS an arithmetic sequence, and the common difference is 2/3.