To determine the sequence for the pattern based on the first four terms visible in the figure, let’s analyze the number of dots:
- Identify the dots in each of the first four terms based on the visual representation.
- Analyze how the number of dots increases from one term to the next to find a numerical pattern.
Since I don't have access to the visual figure showing the number of dots, I'll describe a typical approach to deriving the pattern:
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Identify the first four terms - You would count the dots displayed, such as:
- Term 1: n1 dots
- Term 2: n2 dots
- Term 3: n3 dots
- Term 4: n4 dots
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Look for a relationship - Check how each term relates to the previous one:
- Observe if there's a constant difference (arithmetic sequence).
- Observe if there's a common ratio (geometric sequence).
- It might also be quadratic or follow another non-linear pattern.
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Determine the nth term (Tn) - Once you discern the pattern, formulate the general term for the sequence.
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Calculate the 25th term (T25) using the formula derived.
For illustrative purposes, let’s assume a hypothetical sequence where:
- Term 1: 1 dot
- Term 2: 4 dots
- Term 3: 9 dots
- Term 4: 16 dots
This appears to follow the formula \( T(n) = n^2 \):
- T(1) = \( 1^2 = 1 \)
- T(2) = \( 2^2 = 4 \)
- T(3) = \( 3^2 = 9 \)
- T(4) = \( 4^2 = 16 \)
To find the 25th term:
- T(25) = \( 25^2 = 625 \)
In the case above, 625 does not match your options A-D. So, be sure to check the specific pattern in your visual figure.
Final Step: Choose among options A, B, C, or D based on your analysis of dots for the 25th term according to the formula you derive.
If none of the analysis above matches, please provide the specific number of dots in the first few terms if you can.
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