What reasoning might a student use to apply deductive reasoning to complete the pattern 2, 4, 8, 16, 32, 64, ____?

The reasoning behind choosing to recognize that the pattern involves multiplication by 2 is sound and directly relates to identifying the underlying mechanism of the sequence. The numbers given—2, 4, 8, 16, 32, and 64—are all powers of 2. Each number in the sequence is obtained by multiplying the previous number by 2:

• 2 multiplied by 2 gives 4

• 4 multiplied by 2 gives 8

• 8 multiplied by 2 gives 16

• 16 multiplied by 2 gives 32

• 32 multiplied by 2 gives 64

Following this pattern of consistent multiplication, the next number can be determined by multiplying 64 by 2, which yields 128.

Recognizing this pattern allows the student to predict the continuation of the sequence correctly. Thus, identifying multiplication by 2 is the most accurate reasoning to deduce the next term in the series.

In contrast, checking for prime numbers or identifying even or odd numbers does not directly relate to the multiplication aspect that forms the pattern. A quadratic relationship could imply a different growth pattern such as a parabolic sequence, which does not apply here—reinforcing why understanding the concept of multiplication