Write down the next term in each of the following patterns: $$ 3.1 .11 ; 2 ; 4 ; 2 ; 9 ; 2 ; 16 ; 2 ; 25 ; 2 ; \ldots $$ $$ 3.1 .2 \frac{2+1}{3^{2}-3} ; \frac{3+1}{4^{2}-3} ; \frac{4+1}{5^{2}-3} ; \frac{5+1}{6^{2}-3} ; \ldots \ldots $$

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Let's analyze each pattern step by step to find the next term.

### Pattern 1: $$ 3.1, 0.11, 2, 4, 2, 9, 2, 16, 2, 25, 2, \ldots $$

1. **Identify the sequence:**
   - The sequence alternates between two types of terms: one set of numbers and the number 2.
   - The first set of numbers is: $$ 3.1, 0.11, 2, 4, 9, 16, 25 $$.
   - The second set is consistently $$ 2 $$.

2. **Analyze the first set:**
   - The first set of numbers appears to be perfect squares:
     - $$ 3.1 $$ does not fit the pattern.
     - $$ 0.11 $$ does not fit the pattern.
     - $$ 2 = 1^2 + 1 $$
     - $$ 4 = 2^2 $$
     - $$ 9 = 3^2 $$
     - $$ 16 = 4^2 $$
     - $$ 25 = 5^2 $$

3. **Next term in the first set:**
   - Following the pattern of perfect squares, the next term after $$ 25 $$ (which is $$ 5^2 $$) would be $$ 6^2 = 36 $$.

4. **Next term in the overall sequence:**
   - Since the sequence alternates, the next term after $$ 25 $$ (which is followed by $$ 2 $$) will be $$ 36 $$.

### Conclusion for Pattern 1:
The next term is $$ 36 $$.

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### Pattern 2: $$ 3.1, 0.2, \frac{2+1}{3^{2}-3}, \frac{3+1}{4^{2}-3}, \frac{4+1}{5^{2}-3}, \frac{5+1}{6^{2}-3}, \ldots $$

1. **Identify the sequence:**
   - The terms are of the form $$ \frac{n+1}{(n+2)^2 - 3} $$ where $$ n $$ starts from $$ 2 $$.

2. **Analyze the terms:**
   - For $$ n = 2 $$: $$ \frac{2+1}{3^2 - 3} = \frac{3}{6} = 0.5 $$
   - For $$ n = 3 $$: $$ \frac{3+1}{4^2 - 3} = \frac{4}{13} $$
   - For $$ n = 4 $$: $$ \frac{4+1}{5^2 - 3} = \frac{5}{22} $$
   - For $$ n = 5 $$: $$ \frac{5+1}{6^2 - 3} = \frac{6}{33} $$

3. **Next term in the sequence:**
   - For $$ n = 6 $$: 
   $$
   \frac{6+1}{7^2 - 3} = \frac{7}{49 - 3} = \frac{7}{46}
   $$

### Conclusion for Pattern 2:
The next term is $$ \frac{7}{46} $$.

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### Final Answers:
1. The next term in the first pattern is $$ 36 $$.
2. The next term in the second pattern is $$ \frac{7}{46} $$.
The next term in the first pattern is 36. The next term in the second pattern is 7/46.

Write down the next term in each of the following patterns:

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