To find the next number in the sequence, we need to look for a pattern in the given numbers. Let’s break down the numbers:
- The odd indexed numbers are: 1, 7, 2, 8
- The even indexed numbers are: 125, 750, 225
If we analyze the odd indexed numbers, we see they are increasing: (1 to 7) and then (2 to 8). Following this pattern, the next odd indexed number after 8 should be 3.
Now, looking at the even indexed numbers (125, 750, and 225), we can see a pattern based on multiplication and the involvement of 25s; specifically:
- 125 = 1 x 125
- 750 = 7 x 107.14 (approx)
- 225 = 2 x 112.5 (approx)
However, instead of deriving the next even number in such a convoluted way, we can rather focus on the recurring increase of the first digit in the sequence to provide a simpler prediction on what the neighboring number should be.
Thus, the next even indexed number after 225 should be based on increasing the base 25 pattern, leading to 975, since increasing around the base of 25 while using the same index format could give us that increase.
Combining our findings, the sequence following our discovered patterns leads us to conclude that the next number after 8 could reasonably be: 3
So, if we were to arrange the next full sequence, it could either follow this odd/even differentiation and potentially yield: 975
In conclusion, by determining both parts of this sequence collectively, the anticipated next number in the sequence is 3.