The missing number in the sequence 25, 49, 81, ___, 169, 225 is 121.
Identifying the Pattern
The sequence consists of perfect squares. Let's break it down:
- 25 = 52
- 49 = 72
- 81 = 92
- 169 = 132
- 225 = 152
We can see the bases of the squares (5, 7, 9, 13, 15) are consecutive odd numbers except for a gap after 9. Filling this gap, we recognize that the correct base number should be an odd number.
Determining the Missing Number
To continue the sequence of odd numbers, the number following 9 should be 11. Therefore, the missing number is:
- 112 = 121
Corrected Sequence
Based on the pattern identified, the corrected sequence would be:
| Number | Square Root |
|---|---|
| 25 | 5 |
| 49 | 7 |
| 81 | 9 |
| 121 | 11 |
| 169 | 13 |
| 225 | 15 |
This revised sequence shows the squares of consecutive odd numbers, thereby completing the pattern. The reference sequence 25, 49, 81, 121, 169, 225 confirms our finding.
