Praxis Dashboard

y = 3x + 1

In this sequence, each number can be expressed as a function of its preceding number. Specifically, y can be represented in terms of x as y = 3x + 1, which accurately reflects the relationship observed in the list.

A) y = x + 3

This option suggests that y is simply 3 units more than x, which does not correspond to the pattern in the list. Testing this formula with the numbers in the list reveals inconsistencies, indicating that it does not fit the sequence.

B) y = 2x + 1

While this option proposes a linear relationship, it does not accurately describe the transformation between x and y in the provided list. Substituting values from the sequence shows that it fails to produce the correct subsequent numbers.

C) y = 3x - 1

This formula implies that y is derived from x with a constant subtraction, which does not align with the observed pattern in the sequence. Evaluating it against the numbers in the list demonstrates that it does not yield valid results.

D) y = 3x + 1

This option correctly captures the relationship between x and y based on the sequence presented. By substituting each x value (5, 14, 41, 122) into the formula, we find that it accurately predicts the corresponding y values (14, 41, 122, 365), confirming its validity.

E) y = 3x + 2

This option suggests a relationship that adds 2 to three times x, which does not fit the transformation observed in the list. Testing this formula against the numbers reveals that it does not produce the expected results.

Conclusion

The relationship y = 3x + 1 is the only option that consistently matches the pattern established by the numbers in the list. All other options fail to accurately describe how each number relates to its predecessor, confirming that option D is the correct choice.