Step 1: Understanding the Concept:
We are given a sequence of numbers and need to find the next term by identifying the underlying pattern.
Step 2: Key Formula or Approach:
The numbers in the sequence are easily recognizable as perfect squares. The key is to analyze the sequence of the base numbers that are being squared.
Step 3: Detailed Explanation:
Let's write each term in the sequence as a square:
- \(25 = 5^2\)
- \(49 = 7^2\)
- \(121 = 11^2\)
- \(169 = 13^2\)
The sequence of the base numbers is 5, 7, 11, 13.
This is a sequence of consecutive prime numbers, starting from 5.
- The prime number after 5 is 7.
- The prime number after 7 is 11.
- The prime number after 11 is 13.
To find the next term in the main sequence, we need to find the next prime number after 13.
The next prime number is 17.
The missing term in the sequence is the square of this prime number:
\[ 17^2 = 289 \]
Let's check the options. 289 is option (C). To verify, the next prime after 17 is 19, and \(19^2 = 361\), which is option (A). The term after the missing one would be 361.
Step 4: Final Answer:
The missing number is \(17^2 = 289\), which corresponds to option (C).