The common ratio in a geometric sequence can be found by dividing any term by the previous term. In the sequence provided, we can calculate the common ratio as follows:
- The second term (4) divided by the first term (2) gives us 4 ÷ 2 = 2.
- The third term (8) divided by the second term (4) gives us 8 ÷ 4 = 2.
- The fourth term (16) divided by the third term (8) gives us 16 ÷ 8 = 2.
- The fifth term (32) divided by the fourth term (16) gives us 32 ÷ 16 = 2.
- The sixth term (64) divided by the fifth term (32) gives us 64 ÷ 32 = 2.
As we can see, the ratio between each pair of successive terms is consistently 2. Therefore, the common ratio for the sequence 2, 4, 8, 16, 32, 64 is 2.