100, 81, 64, 49, ?, 25
Sequence Pattern Identification
The sequence provided is 100, 81, 64, 49, ?, 25. The task is to find the number that replaces the question mark.
Analyzing the Number Sequence
Observe the relationship between the consecutive terms:
- 100 is the square of 10 ($10^2$)
- 81 is the square of 9 ($9^2$)
- 64 is the square of 8 ($8^2$)
- 49 is the square of 7 ($7^2$)
- 25 is the square of 5 ($5^2$)
The pattern reveals that the sequence consists of perfect squares of decreasing integers, starting from 10.
Determining the Missing Term
The sequence of bases for the squares is 10, 9, 8, 7, ... , 5.
The missing base in this descending sequence is 6.
Therefore, the missing term in the sequence is the square of 6:
Missing Term = $6^2 = 6 \times 6 = 36$.
The sequence is $10^2, 9^2, 8^2, 7^2, 6^2, 5^2$.
Final Answer
The number 36 correctly fits the pattern of perfect squares in the descending sequence.
Similar Questions
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Important Questions from Number Series
Select the number from among the given options that can replace the question mark (?) in the following series.
37, 52, 74, 104, 143, ?
Select the number that can replace the question mark (?) in the following series.
17, 19, 22, 27, 34, 45, 58,?Select the number from among the given options that can replace the question mark (?) in the following series.
10, 14, 31, 35, 73, 77, ?
Select the number from among the given options that can replace the question mark (?) in the following series.
215, 231, 256, 292, ?
Select the number from among the given options that can replace the question mark (?) in the following series.
6, 6, 8, 24, 28, 140, ?
