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Answer:
For the given number sequences, let's try to identify the patterns:
1. 1, 2, 1, 3, 2, 8, 7
- If we look at the differences between the numbers:
2 - 1 = 1
1 - 2 = -1
3 - 1 = 2
2 - 3 = -1
8 - 2 = 6
7 - 8 = -1
On observing the differences, we can see a pattern where the numbers alternate between adding and subtracting 1, then 2, then 3, and so on:
1 + 2 - 1 + 3 - 2 + 4 - 3 = 35
1 + 2 - 1 + 3 - 2 + 4 = 34
2. 2, 2, 1, 2, 1, 3, 2, 8, 7
- If we analyze the differences in this sequence:
2 - 2 = 0
1 - 2 = -1
2 - 1 = 1
1 - 2 = -1
3 - 1 = 2
2 - 3 = -1
8 - 2 = 6
7 - 8 = -1
Similarly, we can see a pattern where the numbers alternate between adding and subtracting 0, then 1, then -1, then 2, and so on:
2 + 1 - 1 + 2 - 1 + 3 - 2 + 4 - 3 = 35
2 + 1 - 1 + 2 - 1 + 3 - 2 + 4 = 34
3. 20, 24, 12, 16, 8, 12, 6, 10
- Analyzing the differences:
24 - 20 = 4
12 - 24 = -12
16 - 12 = 4
8 - 16 = -8
12 - 8 = 4
6 - 12 = -6
10 - 6 = 4
In this sequence, the pattern seems to involve alternating between subtracting and adding 4, then -12, then 4, then -8, and so on:
20 - 4 + 12 - 16 + 8 - 12 + 6 - 10 = 5
20 + 4 - 12 + 16 - 8 + 12 - 6 = 7
These patterns help understand how the solutions were obtained for each sequence.