Generate the sequence: 1,3,5,4,10,7,15,8,20,9,18,24,31,14,28,22,42,33,35,46......
To generate the given sequence: 1, 3, 5, 4, 10, 7, 15, 8, 20, 9, 18, 24, 31, 14, 28, 22, 42, 33, 35, 46......, we can observe a pattern and use it to generate the subsequent terms.
Let's break down the sequence into multiple parts and identify the patterns within each part:
Part 1: 1, 3, 5, 4
Here, the numbers are increasing by 2 in the first two terms and then decreasing by 1 in the third term.
Part 2: 10, 7, 15, 8, 20, 9
In this part, the numbers are increasing and decreasing alternatively. The pattern seems to be that the numbers increase by 3, decrease by 2, increase by 7, decrease by 1, increase by 11, decrease by 1, and so on.
Part 3: 18, 24, 31
Here, the numbers are increasing consecutively: 18, 24, 31. We can notice that each term is the sum of the previous term and an increment by 6.
Part 4: 14, 28, 22, 42
In this part, the numbers are increasing and decreasing alternatively. The pattern appears to be that the numbers increase by 14, decrease by 6, increase by 20, and decrease by 1.
Based on the patterns observed in each part, we can develop the following rule to generate the sequence:
1. The sequence starts with 1.
2. The first three terms increase by 2, and the fourth term decreases by 1.
3. From the fourth term onwards, the pattern alternates between:
- Increasing and decreasing by varying amounts.
- Increasing consecutively with a fixed increment.
4. Repeat steps 2 and 3 to generate subsequent terms of the sequence.
Now, let's generate the next terms of the sequence using this rule:
Next term: 10 + 3 = 13 (increasing by 3)
Next term: 13 - 2 = 11 (decreasing by 2)
Next term: 11 + 7 = 18 (increasing by 7)
Next term: 18 - 1 = 17 (decreasing by 1)
Next term: 17 + 11 = 28 (increasing by 11)
Continuing this process, we can generate the remaining terms of the given sequence.