Identify the pattern in the sequence: 1, 4, 9, 16, 25, ...
Find the 10th term in the sequence. Explain your reasoning.
Answer (2)
The sequence consists of perfect squares: 1, 4, 9, 16, and 25 correspond to 1 2 , 2 2 , 3 2 , 4 2 , and 5 2 . The formula for the n-th term is n 2 , and the 10th term is therefore 1 0 2 = 100 .
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The sequence given is: 1, 4, 9, 16, 25, ...
To identify the pattern, we need to determine how each number in the sequence is derived. If we observe the sequence closely, each term appears to be a perfect square:
The first term is 1 2 = 1 .
The second term is 2 2 = 4 .
The third term is 3 2 = 9 .
The fourth term is 4 2 = 16 .
The fifth term is 5 2 = 25 .
It becomes evident that each term in the sequence is the square of a natural number increasing sequentially.
To find the 10th term of the sequence, we follow the same pattern:
The 10th term will be 1 0 2 .
Calculating that: 1 0 2 = 100
Thus, the 10th term in the sequence is 100.
This recognition shows us that the pattern is based on squaring natural numbers in an increasing order.
