To determine whether the sequence 3, 12, 21, 30 is a geometric sequence, we first need to understand what a geometric sequence is. In a geometric sequence, each term after the first is found by multiplying the previous term by a constant called the common ratio.
Let’s examine the sequence:
- The first term is 3.
- The second term is 12.
- The third term is 21.
- The fourth term is 30.
Next, we calculate the ratios between consecutive terms:
- Common ratio between the first and second term: 12/3 = 4
- Common ratio between the second and third term: 21/12 = 1.75
- Common ratio between the third and fourth term: 30/21 = 1.42857
Since these ratios are not the same, we can conclude that the sequence 3, 12, 21, 30 is not a geometric sequence.