To find the next number in the series, let’s first analyze the pattern. The given numbers are: 6, 18, 20, 10, 30, 32, 16.
If we look closely, we can separate the series into two alternating sequences:
- The first sequence: 6, 20, 30, 16
- The second sequence: 18, 10, 32
Now, we can analyze each sequence:
1. For the first sequence (6, 20, 30, 16):
- 6 + 14 = 20
- 20 + 10 = 30
- 30 – 14 = 16
It seems that there is a pattern where we are alternating between adding and subtracting. The final number (16) does not give us an immediate next number, but if we followed the sequence of alternating differences, the next operation would logically lead us to add.
2. Now, looking at the second sequence (18, 10, 32):
- 18 – 8 = 10
- 10 + 22 = 32
This sequence does not follow a consistent addition or subtraction pattern that’s easy to decipher. However, if we look at the nature of the numbers and try to keep the alternating pattern with the first sequence, we would stick with our first finding.
Thus, if we follow that first sequence’s logic, where we seem to alternate the operations, and predict we might add a number larger than the last addition (which was 10), we may estimate the next number.
Based on our calculations and observations, we see the next number is expected to be 30, reaching us back to the flow of the sequence. Thus the answer could be: