Answer:

Sammy and Juan are both correct.

Sammy used explicit notation and Juan used recursive notation.

Jenny is incorrect because she did not use 1 as the first t number as indicated in the table in her equation.

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]