If the first 4 terms of a geometric sequence are $$ \{7,21,63,189\} $$, then the formula for the $$ n^{t h} $$ term in the sequence is $$ \begin{array}{ll}\text { b.) } a_{n}=3 \cdot(n-1)^{7} \ \text { b.) } a_{n}=3 \cdot 7^{n-1} \ \text { c.) } a_{n}=7 \cdot 3^{n-1} \ \text { d.) } a_{n}=7 \cdot(n-1)^{3}\end{array} $$

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To determine the formula for the $$ n^{\text{th}} $$ term of the geometric sequence $$ \{7, 21, 63, 189\} $$, follow these steps:

1. **Identify the First Term ($$ a_1 $$)**:
   - The first term is $$ 7 $$.

2. **Determine the Common Ratio ($$ r $$)**:
   - $$ r = \frac{21}{7} = 3 $$
   - To confirm, $$ \frac{63}{21} = 3 $$ and $$ \frac{189}{63} = 3 $$, so the common ratio is consistently $$ 3 $$.

3. **Use the Formula for the $$ n^{\text{th}} $$ Term of a Geometric Sequence**:
   $$
   a_n = a_1 \cdot r^{n-1}
   $$
   Substituting the known values:
   $$
   a_n = 7 \cdot 3^{n-1}
   $$

**Among the given options, the correct formula is:**

**c.) $$ a_n = 7 \cdot 3^{n-1} $$**
The formula for the $$ n^{\text{th}} $$ term is $$ a_n = 7 \cdot 3^{n-1} $$.

If the first 4 terms of a geometric sequence are , then the
formula for the term in the sequence is

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