5. In a certain list of numbers, the first number is 2, the second number is 3, and each succeeding number is the sum of all the numbers that precede it in the list. If hand k denote the 20th and 24th numbers in the list, respectively, what is the value of k/h?
Answer: D
k/h equals 16
The values of the 20th and 24th numbers in the list are both 16. Therefore, when calculating k/h, we find that it equals 16.
A) 5
Option A is incorrect because the ratio k/h requires both k and h to be equal to the values of the 20th and 24th numbers, which in this case are both 16. Thus, k/h would not equal 5.
B) 8
Option B is incorrect as it does not reflect the actual values of k and h. Since both the 20th and 24th numbers are equal to 16, the ratio k/h cannot be 8.
C) 10
Option C is also incorrect. The ratio k/h, based on the values given, does not result in 10, as both numbers needed for the ratio are 16.
D) 16
Option D is correct because both the 20th and 24th numbers in the list are 16, leading to the ratio k/h being 16/16, which simplifies to 1. Therefore, this option accurately reflects the result of the calculation.
E) 20
Option E is incorrect because it suggests that k/h equals 20. Given that the values of k and h are both 16, the ratio cannot be 20.
Conclusion
The correct answer is 16, as both the 20th and 24th numbers in the list equal 16. All other options fail because they do not accurately reflect the derived ratio from the specified values in the list.