Explanations:A geometric progression is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio. In this problem, the common ratio is 2, meaning each number in the sequence is double the previous one. The sequence starts with 1, and the next terms are 2, 4, 8, and so on.
To determine which pair of numbers is part of the pattern, we need to check if the second number in each pair is double the first number. This is because the rule given is "double the number," which means each term in the sequence is obtained by multiplying the previous term by 2.
Let's analyze each pair:
For the pair (42, 84):
42 doubled is 84, which means 42 * 2 = 84. This pair follows the doubling rule and is part of the pattern.
For the pair (26, 51):
26 doubled is 52, not 51. This pair does not follow the doubling rule and is not part of the pattern.
For the pair (33, 65):
33 doubled is 66, not 65. This pair does not follow the doubling rule and is not part of the pattern.
For the pair (31, 61):
31 doubled is 62, not 61. This pair does not follow the doubling rule and is not part of the pattern.
Therefore, the only pair that follows the doubling rule and is part of the pattern is (42, 84).