To find the next number in the sequence 256, 196, 144, 100, 64, 36, 16, we can start by examining the numbers and identifying any patterns or relationships between them.
These numbers can be expressed as perfect squares of descending integers:
- 256 is 162
- 196 is 142
- 144 is 122
- 100 is 102
- 64 is 82
- 36 is 62
- 16 is 42
From this perspective, we see that every number is the square of an even integer, decreasing by 2 each time:
- 16, 14, 12, 10, 8, 6, 4
Following this pattern, the next even integer to consider would be 2. Thus, we calculate:
- 22 = 4
Therefore, the next number in the sequence should be 4.