Which of these is not a geometric sequence?
4, 12, 20, 28, ...
5, 15, 45, 135, ...
3, 6, 12, 24, ...
250, 50, 10, 2, ....
3, 6, 12, 24, ... (not a geometric sequence)
y = ax, where a is greater than zero but not equal to 1 and x is an exponent
1. exponential decay
2. exponential function decline of a quantity that is directly proportional to the amount present
3. exponential growth
2. exponential function
To determine which of the given sequences is not a geometric sequence, we need to check if there is a common ratio between consecutive terms.
In a geometric sequence, each term is obtained by multiplying the previous term by a fixed value called the common ratio.
Let's check each sequence:
1. 4, 12, 20, 28, ...
To find the common ratio, we divide any term by the previous term. For example:
12/4 = 3,
20/12 = 5/3 ≈ 1.67,
28/20 = 7/5 = 1.4
As we can see, the common ratio is not the same for all terms, which means this sequence is not a geometric sequence.
2. 5, 15, 45, 135, ...
Similarly, let's find the common ratio:
15/5 = 3,
45/15 = 3,
135/45 = 3
In this case, we have a constant common ratio of 3, which means this sequence is a geometric sequence.
3. 3, 6, 12, 24, ...
Again, let's find the common ratio:
6/3 = 2,
12/6 = 2,
24/12 = 2
This sequence also has a constant common ratio of 2, so it is a geometric sequence.
4. 250, 50, 10, 2, ....
Finally, let's find the common ratio:
50/250 = 1/5 = 0.2,
10/50 = 1/5 = 0.2,
2/10 = 1/5 = 0.2
As with the previous sequences, this sequence also has a constant common ratio of 0.2, which means it is a geometric sequence.
Therefore, the sequence that is not a geometric sequence is the first one: 4, 12, 20, 28, ...