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Answer :
To find the next three numbers in each sequence, we need to identify the pattern or rule governing each sequence.
Sequence A: 2, 5, 11, 17, 20, 23
Start by looking at the differences between consecutive terms: 5 - 2 = 3, 11 - 5 = 6, 17 - 11 = 6, 20 - 17 = 3, 23 - 20 = 3.
We notice the differences alternate between +3 and +6.
Continuing this pattern from the last number, 23, we add 6 to get 29, then 3 to get 32, and again 6 to get 38.
So, the next three numbers in the sequence are 29, 32, and 38.
Sequence B: 4, 5, 8, 13, 20, 29, 40
Calculate the differences between consecutive terms: 5 - 4 = 1, 8 - 5 = 3, 13 - 8 = 5, 20 - 13 = 7, 29 - 20 = 9, 40 - 29 = 11.
The differences are increasing by 2 each time: 1, 3, 5, 7, 9, 11.
The next difference should be 13, so add 13 to 40 to get 53.
The next difference after 13 should be 15, so add 15 to 53 to get 68.
Finally, add 17 (the next in the pattern) to 68 to get 85.
Thus, the next three numbers are 53, 68, and 85.
Sequence C: 1, 2, 4, 8, 16, 32, 64
Observe that each term is obtained by multiplying the previous term by 2: \(1 \times 2 = 2\), \(2 \times 2 = 4\), \(4 \times 2 = 8\), and so on.
Continue this pattern: \(64 \times 2 = 128\), \(128 \times 2 = 256\), and \(256 \times 2 = 512\).
Thus, the next three numbers in the sequence are 128, 256, and 512.
In summary, by analyzing the differences or multiplicative factors in each sequence, we can predict the following numbers:
- For Sequence A, the numbers are 29, 32, and 38.
- For Sequence B, the numbers are 53, 68, and 85.
- For Sequence C, the numbers are 128, 256, and 512.
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