Given $$ -4 ;-7 ;-10 ;-13 ; \ldots $$ Determine the rule (formula) to describe the general term $$ T_{n} $$.

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To find the general term $$ T_n $$ for the sequence $$ -4, -7, -10, -13, \ldots $$, we first observe the pattern in the sequence.

1. **Identify the first term**: The first term $$ T_1 = -4 $$.
2. **Identify the common difference**: 
   - The difference between the first term and the second term is $$ -7 - (-4) = -3 $$.
   - The difference between the second term and the third term is $$ -10 - (-7) = -3 $$.
   - The difference between the third term and the fourth term is $$ -13 - (-10) = -3 $$.

Thus, the common difference $$ d = -3 $$.

3. **Use the formula for the $$ n $$-th term of an arithmetic sequence**:
   The general formula for the $$ n $$-th term of an arithmetic sequence is given by:
   $$
   T_n = T_1 + (n - 1) \cdot d
   $$
   where $$ T_1 $$ is the first term and $$ d $$ is the common difference.

4. **Substituting the values**:
   - $$ T_1 = -4 $$
   - $$ d = -3 $$

Therefore, we have:
   $$
   T_n = -4 + (n - 1)(-3)
   $$

5. **Simplifying the expression**:
   $$
   T_n = -4 - 3(n - 1)
   $$
   $$
   T_n = -4 - 3n + 3
   $$
   $$
   T_n = -3n - 1
   $$

Thus, the formula for the general term $$ T_n $$ of the sequence is:
$$
\boxed{T_n = -3n - 1}
$$
The formula for the general term $$ T_n $$ of the sequence is $$ T_n = -3n - 1 $$.

Given \( -4 ;-7 ;-10 ;-13 ; \ldots \) Determine the rule (formula) to describe the general term \( T_{n} \).

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