Determine whether the sequence is arithmetic geometric or neither 1/2,7/6,11/6,5/2

1 answer

To determine whether a sequence is arithmetic, geometric, or neither, we need to check if there is a common difference or a common ratio between consecutive terms.

Let's check the sequence:

1/2, 7/6, 11/6, 5/2

To determine if the sequence is arithmetic, we check if there is a common difference between consecutive terms. We subtract each term from the previous term to check for a pattern:

7/6 - 1/2 = 3/6 = 1/2
11/6 - 7/6 = 4/6 = 2/3
5/2 - 11/6 = 15/6 - 11/6 = 4/6 = 2/3

The differences between consecutive terms are not constant, so the sequence is not arithmetic.

Next, let's check if the sequence is geometric. We check if there is a common ratio between consecutive terms. We divide each term by the previous term and check for a pattern:

(7/6) / (1/2) = (7/6) * (2/1) = 14/6 = 7/3
(11/6) / (7/6) = (11/6) * (6/7) = 11/7
(5/2) / (11/6) = (5/2) * (6/11) = 30/22 = 15/11

The ratios between consecutive terms are not constant, so the sequence is not geometric.

Since the sequence does not show a constant difference or a constant ratio between consecutive terms, it is neither an arithmetic sequence nor a geometric sequence.