Explanation: In this problem, we are dealing with a number pattern where each number is double the previous one. This is a geometric progression with a common ratio of 2. The sequence starts with 1 and each subsequent number is obtained by multiplying the previous number by 2. The sequence looks like this: 1, 2, 4, 8, 16, 32, 64, 128, and so on.
The task is to identify which pair of numbers fits this pattern. The correct answer is option A: 42, 84. Although 42 is not part of the original sequence starting from 1, the pair itself follows the doubling rule. The number 84 is indeed double 42, which satisfies the rule of the pattern.
To understand why the other options are incorrect, let's examine them one by one:
- Option B: 26, 51. The number 51 is not double 26. The correct double of 26 would be 52, not 51. Therefore, this pair does not follow the doubling rule.
- Option C: 33, 65. The number 65 is not double 33. The correct double of 33 would be 66, not 65. Therefore, this pair does not follow the doubling rule.
- Option D: 31, 61. The number 61 is not double 31. The correct double of 31 would be 62, not 61. Therefore, this pair does not follow the doubling rule.
In summary, the correct answer is option A: 42, 84, because it is the only pair that follows the doubling rule, even though 42 is not part of the original sequence starting from 1. The key concept here is recognizing the doubling pattern and ensuring that the second number in the pair is exactly double the first number.