Answer:

Sammy and Jenny are both incorrect because they used explicit notation.

Juan is correct because he shows a constant change of 8.  Juan used recursive notation.

However, Sammy would be correct if t = the term number and t begins at 1. 

Jenny would be correct if her t begins at 0, but if not noted this is assumed incorrect. 

Teacher’s Note:

In the recursive form of pattern generalization, students focus on the rate of change from one element to the next. 

(Juan would continue adding 8 to determine the next number in the sequence.) 

The explicit form of pattern generalization involves developing a rule or formula that highlights the relationship between the independent variable (the number representing the position of the term in the sequence) and the dependent variable (the number in the sequence).

(Sammy multiplied the term by 8 and added four to determine the sequence number.)[1]