To determine the number that completes the pattern, we first need to analyze the given sequence: 66, 73, 13, 21, 52, 10, 20.
Let’s break down the pairs in the sequence:
- 66 to 73: The difference is +7.
- 73 to 13: The difference is -60.
- 13 to 21: The difference is +8.
- 21 to 52: The difference is +31.
- 52 to 10: The difference is -42.
- 10 to 20: The difference is +10.
It seems that the numbers alternate between increasing and decreasing significantly:
- The first increase is by +7.
- A dramatic decrease of -60 follows.
- Next is a moderate increase of +8.
- The pattern shifts again with a larger increase of +31.
- Then, a larger decrease of -42 occurs.
- Finally, an increment of +10 finishes this part of the sequence.
If we look for a potential number to follow 20, we might want to consider continuing the pattern of alternating increases and decreases. We notice that previous increases ranged from +7 to +31, but they are increasing in magnitude each time.
If we take into account the fluctuation and try to match the previous patterns of decrease:
- The last noted increase was +10.
- Following the pattern, a decrease could return us to a prior position.
To find a number following 20, let’s consider a decrease similar in pattern to the previous shifts. Taking into account the sequence behaviors and seeking a consistent decrease could lead us into the negative side. For example, if we try a decrease of -10 (which fits the overall rhythm of the previous decreases), we find that:
20 – 10 = 10
However, since 10 is already present in the sequence, another approach should be considered. If we start from 20 and use the pattern logic, perhaps a larger decrease is necessary.
Let’s try something similar to the average of prior reductions. Taking down 20 by, say, 15 units, positions us at:
20 – 15 = 5
The number needed to complete the pattern could logically be concluded to be 5, connecting the lower end of fluctuations in the sequence.
In summary, the number that possibly completes this sequence might very well be: