Question

Determine whether the sequence is geometric. example is 10,20,30,40....... The ratio .

Answer 1

The sequence 10, 20, 30, 40... is not geometric because the ratios between consecutive terms are not consistent, which is a requirement for a sequence to be classified as geometric.

Step-by-step explanation:

To determine whether a sequence is geometric, we need to establish if there is a common ratio between successive terms. For this example, the sequence given is 10, 20, 30, 40.... We examine the ratio between successive terms:

• The ratio of the second term to the first term is 20/10 = 2.
• The ratio of the third term to the second term is 30/20 = 1.5.
• The ratio of the fourth term to the third term is 40/30 ≈ 1.33.

Since the ratios are not consistent, the sequence is not geometric. In a geometric sequence, the ratio between each pair of successive terms must be the same. Therefore, it fails the criteria of a geometric sequence where a constant ratio is a fundamental characteristic.