This problem involves recognizing the pattern of the sequence given and predicting its future terms. Let's analyze:

The terms are: $9, 16, 25, 36, 49, 64, \dots$

Observations:

Each term is a perfect square:

• $9 = 3^2$
• $16 = 4^2$
• $25 = 5^2$
• $36 = 6^2$
• $49 = 7^2$
• $64 = 8^2$

The $n$-th term is given by: $T_n = n^2$

Now, let’s calculate:

• The 14th term: $T_{14} = 14^2 = 196$
• The 28th term: $T_{28} = 28^2 = 784$

Final Answer:

• 14th term = 196
• 28th term = 784

Would you like an explanation of the process or help with similar problems?

Related Questions:

1. What is the formula to find the $n$-th term of a sequence of perfect squares?
2. Can you derive the sum of the first $n$ perfect squares?
3. What is the pattern in the difference between consecutive perfect squares?
4. How would this pattern change if the sequence was cubes instead of squares?
5. Can this sequence be represented as a geometric progression?

Tip:

To quickly identify a pattern, always look at differences or relationships between terms (e.g., multiplication, addition, squares, cubes, etc.).