The sequence you’ve provided is 2, 4, 8, 16, 32, 64. To determine the common ratio between successive terms in this sequence, we need to look at how each term relates to the one before it.
The common ratio (r) can be found by dividing any term in the sequence by its preceding term. Let’s calculate this:
- r = 4 / 2 = 2
- r = 8 / 4 = 2
- r = 16 / 8 = 2
- r = 32 / 16 = 2
- r = 64 / 32 = 2
As you can see, the ratio is consistently 2 across all terms. Therefore, we can conclude that the common ratio of the sequence is 2.
This sequence is an example of a geometric progression, which is characterized by a constant ratio between each term. In this case, every number is obtained by multiplying the previous term by 2, resulting in an exponential increase in values.