In the sequence 3, 5, 9, 17, 33, the change from one number to the next can best be described how?

The sequence 3, 5, 9, 17, 33 reveals a pattern in how each number increases from the previous one. Observing the differences between successive terms provides clarity. The differences are as follows:

• From 3 to 5, the change is 2.

• From 5 to 9, the change is 4.

• From 9 to 17, the change is 8.

• From 17 to 33, the change is 16.

The differences exhibit a specific pattern of doubling—the increase from one term to the next is consistently double the previous increase. This pattern shows that the values are not added in a linear manner, where a constant number is added; instead, the amount added grows exponentially, as each step represents a doubling of the previous increment (2, 4, 8, 16).

This doubling characteristic characterizes exponential growth, as each term increases by a factor related to its position in the sequence. Therefore, the correct answer effectively captures the nature of the sequence, highlighting that the increases illustrate an exponential change rather than a linear or other type of progression.