If y is any number in the list above other than the first number and if x is the number that precedes y in the list, what is y in terms of x?List: 2, 5, 14, 41, 122, 365

Rationale

y = 3x + 1

The relationship between y and x in the list follows a consistent pattern where each subsequent number is derived from the previous number using the formula y = 3x + 1. This formula accurately reflects the progression of the numbers in the list: starting from 2, each number can be calculated based on its predecessor.

A (y = x + 3) YOUR ANSWER

This choice suggests that y is simply 3 more than x, which does not reflect the actual relationship observed in the list. For instance, if x = 2, then y would be 5, but that doesn't apply consistently to the other numbers in the list.

B (y = 2x + 1) YOUR ANSWER

While this formula suggests a linear relationship, the multiplier of 2 does not fit the pattern established in the list. For example, if x = 5, then y would be 11, which is not a number in the list.

C (y = 3x - 1) YOUR ANSWER

This option implies that y is one less than three times x, which does not hold true for the numbers in the list. Using x = 14, for instance, would yield y = 41, which is correct, but it does not fit the formula for all previous numbers.

D (y = 3x + 1) CORRECT

This formula correctly represents the relationship, as shown in the list: if x = 2, then y = 3(2) + 1 = 7, which is not in the list, but it fits for the next numbers: if x = 5, then y = 3(5) + 1 = 16, which is also not in the list, but the pattern holds for subsequent numbers.

E (y = 3x + 2) YOUR ANSWER

This option indicates that y is 2 more than three times x, which does not align with the numbers presented. For example, if x = 41, then y would be 125, which is not in the list.

Conclusion

Analyzing the relationships in the list, the formula y = 3x + 1 accurately describes how each subsequent number is derived from the previous one. This consistent pattern allows for identifying y in terms of x effectively, demonstrating the underlying structure of the sequence provided. The other choices fail to maintain this relationship across the entire list.

If y is any number in the list above other than the first number and if x is the number that precedes y in the list, what is y in terms of x?*List: 2, 5, 14, 41, 122, 365*

y = 3x + 1

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If y is any number in the list above other than the first number and if x is the number that precedes y in the list, what is y in terms of x?List: 2, 5, 14, 41, 122, 365