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Hello, i have a study guide with a few number sequence examples that are solved, yet i can't understand how the answers are that way. Any insight into the possible patterns would be appreciated!
1) 1,2,1,3,2,8,7(the solution is apparently 35 and 34)
2) 2,2,1,2,1,3,2,8,7(solutions also 35, 34)
3) 20,24,12,16,8,12,6,10(solutions 5,7)

Sagot :

HELPERNJidn

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.

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