To determine the missing number in the sequence: 1, 16, 100, 169, we first need to analyze the numbers provided.
The numbers in this sequence are perfect squares:
- 1 = 12
- 16 = 42
- 100 = 102
- 169 = 132
Next, we should identify the pattern in the sequence of square roots: 1, 4, 10, and 13. Calculating the differences between these numbers:
- 4 – 1 = 3
- 10 – 4 = 6
- 13 – 10 = 3
The differences alternate between 3 and 6, suggesting that the missing number’s square root could fit into this pattern. To find the missing number, we can also look for the missing perfect square that would fit before 16 and after 1.
If we continue the series: after 1 (which is 12) and before 16 (which is 42), the next perfect square is 9, since 9 = 32.
Therefore, we can conclude that the missing number in the sequence is:
- 9