Generate the sequence: 1,3,5,4,10,7,15,8,20,9,18,24,31,14,28,22,42,35,33,46......
To generate the given sequence, it appears to follow a specific pattern. Let's break it down into segments to better understand the pattern.
Segment 1: 1, 3, 5
Segment 2: 4, 10
Segment 3: 7, 15
Segment 4: 8, 20
Segment 5: 9, 18, 24
Segment 6: 31
Segment 7: 14, 28
Segment 8: 22, 42
Segment 9: 35, 33, 46
Observing the segments, we can see the following patterns:
- In Segment 1, the numbers increase by 2 in each step.
- In Segment 2, the numbers increase by 6 in each step (2 * 3).
- In Segment 3, the numbers increase by 8 in each step (2 * 4).
- In Segment 4, the numbers increase by 12 in each step (2 * 6).
- In Segment 5, the numbers increase by 9 in each step.
- In Segment 6, the number is 31, an outlier.
- In Segment 7, the numbers increase by 14 in each step (2 * 7).
- In Segment 8, the numbers increase by 20 in each step (2 * 10).
- In Segment 9, the numbers increase by 3 in the first step, then decrease by 2 in the next step.
Based on these patterns, we can deduce a general rule for generating the sequence:
- For odd-numbered segments (1st, 3rd, 5th, etc.), the numbers increase by an amount equal to 2 multiplied by the segment number.
- For even-numbered segments (2nd, 4th, 6th, etc.), the numbers increase by (2 * segment number) multiplied by the previous odd-numbered segment's number.
Let's generate a few more terms using this rule to verify if it holds true:
Segment 10: In the 9th segment, the last number was 46. So, in this segment, the numbers should increase by (2 * 9) * 46 = 828.
The next terms in the sequence would be 46 + 828 = 874 and 46 + 2 * 9 * 828 = 1,742.
Hence, the next terms in the sequence according to the pattern are 874, 1,742.
Note: It is important to be aware that the pattern observed may not always hold true for larger segments, as there may be specific outliers or variations in the pattern.