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, we can identify certain patterns and rules that are followed. Let's analyze the sequence step by step:
1. The first three numbers, 1, 3, and 5, form an increasing sequence where each number is the previous number plus 2.
2. The next number, 4, breaks the pattern. It can be seen as the result of subtracting 1 from the previous number (5-1=4).
3. The next four numbers, 10, 7, 15, and 8, appear to form pairs (10, 7) and (15, 8). The first number of each pair is twice the value of the previous number in the sequence, and the second number of each pair is the previous number plus 5.
4. The following four numbers, 20, 9, 18, and 24, can also be grouped into pairs (20, 9) and (18, 24). The pattern is similar to the previous step, where the first number of each pair is twice the value of the previous number, and the second number is the previous number minus or plus 1.
5. Continuing, we have the sequence 31, 14, 28, and 22. Again, we can see pairs (31, 14) and (28, 22). Similar to the previous steps, the first number of each pair is twice the value of the previous number, and the second number is the previous number minus or plus a value.
6. Lastly, we observe three numbers, 42, 35, and 33, forming a pattern. These numbers can be grouped as (42, 35) and (33). Similar to the previous pairs, the first number of each pair is twice the value of the previous number, and the second number is the previous number minus or plus a value.
Hence, the sequence can be generated as follows:
1, 3, 5, 4, 10, 7, 15, 8, 20, 9, 18, 24, 31, 14, 28, 22, 42, 35, 33, 46.