Final answer:
The next number in the sequence 3, 2, 6, 6, 12, 12 is 24. The pattern involves doubling the last repeated number, thus following the sequence: 3 is followed by 2 (two-thirds of 3), then 2 is tripled to get 6, repeated, and then doubled to get 12, which is also repeated. Continuing this, we double the last repeated number, 12, to get 24.
Step-by-step explanation:
The question is asking to determine the next number in the sequence 3, 2, 6, 6, 12, 12. To solve problems like this, we look for patterns in the given sequence. A common method to find the pattern involves looking at the differences between successive numbers or performing operations such as division or multiplication.
By examining the sequence, we notice a pattern where each number (after the first) is either half the subsequent number or twice the preceding number. Starting with 3, the next number is 2, which is two-thirds of 3. Then, to get 6, we multiply 2 by 3. The sequence then repeats this number, 6. After repeating, it doubles to get 12, and again, 12 is repeated.
Following this pattern, we predict that the sequence will continue by doubling the last number repeated, which is 12. Doubling 12 gives us 24, and therefore, we would expect the sequence to be: 3, 2, 6, 6, 12, 12, 24.