20,24,28,32,48
is this sequence arithmetic geometric or neither. If is arithmetic or geometric state the common difference or common ratio. Write the next three terms of the sequence
24-20 = 4 but 48-32 ≠ 4
24/20 = 6/5 but 28/24 ≠ 6/5
so, neither
That pesky 48 throws the sequence for a loop. No idea what's next.
To determine whether the given sequence is arithmetic, geometric, or neither, we need to examine the differences or ratios between consecutive terms.
Let's check the differences between consecutive terms:
24 - 20 = 4,
28 - 24 = 4,
32 - 28 = 4,
48 - 32 = 16.
As we can see, the differences are not constant, indicating that the sequence is not arithmetic.
Now let's check the ratios between consecutive terms:
24 / 20 = 1.2,
28 / 24 = 1.1667,
32 / 28 = 1.1429,
48 / 32 = 1.5.
The ratios are not constant either, meaning that the sequence is not geometric.
Therefore, the given sequence is neither arithmetic nor geometric.
To find the next three terms of the sequence, we can continue extending the pattern we observe in the sequence. Since we determined that the sequence is not arithmetic or geometric, we will need to identify a different pattern.
Looking at the terms, it seems that the sequence is increasing in a somewhat irregular manner. The differences between consecutive terms are not constant, but they are increasing. Let's consider the differences between the terms:
Term1: 20
Term2: 24
Difference: 24 - 20 = 4
Term2: 24
Term3: 28
Difference: 28 - 24 = 4
Term3: 28
Term4: 32
Difference: 32 - 28 = 4
Term4: 32
Term5: 48
Difference: 48 - 32 = 16
The differences between consecutive terms do not seem to follow any specific pattern.
Therefore, we cannot accurately determine the next three terms of the sequence without having more information or a clear pattern to follow.