To determine the common ratio of the given geometric sequence, we can look at the ratio of any two successive terms. In a geometric sequence, each term is obtained by multiplying the previous term by a constant called the common ratio.
Let’s take the first two terms of the sequence: 2 and 4. We can find the common ratio (r) by dividing the second term by the first term:
r = 4 / 2 = 2
Next, let’s verify this with the next pairs of terms:
8 / 4 = 2
16 / 8 = 2
32 / 16 = 2
In each case, the common ratio is consistently 2. This shows that we can repeatedly multiply the previous term by 2 to get the next term in the sequence.
Therefore, the common ratio of the geometric sequence 2, 4, 8, 16, 32 is 2.