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It looks like you're working on finding an explicit formula for a geometric sequence from Khan Academy.

The sequence given is: \( 3, 15, 75, 375, \dots \)

### Steps to find the explicit formula for this geometric sequence:

1. **Identify the first term \( a(1) \):**
   The first term \( a(1) \) is 3.

2. **Find the common ratio \( r \):**
   The common ratio \( r \) is the factor by which you multiply each term to get the next term.
   
   \[
   r = \frac{15}{3} = 5
   \]
   Thus, the common ratio is 5.

3. **Write the explicit formula:**
   The general formula for the \( n \)-th term of a geometric sequence is:

   \[
   a(n) = a(1) \cdot r^{(n-1)}
   \]
   Substituting \( a(1) = 3 \) and \( r = 5 \), the explicit formula becomes:

   \[
   a(n) = 3 \cdot 5^{(n-1)}
   \]

### Final answer:
\[
a(n) = 3 \cdot 5^{(n-1)}
\]

Would you like further details or clarification on any step?

### Related Questions:
1. How would the explicit formula change if the common ratio were negative?
2. What is the 6th term of the geometric sequence?
3. How do you derive the recursive formula for this sequence?
4. How can we determine if a sequence is geometric from its terms?
5. Can you explain how geometric sequences are applied in real-life scenarios?

**Tip:** Always double-check your common ratio by dividing consecutive terms to avoid calculation errors.

Find an explicit formula for the geometric sequence 3, 15, 75, 375,...

Find the explicit formula for the geometric sequence 3, 15, 75, 375 with a common ratio of 5. Learn how to calculate geometric sequences using a step-by-step guide. Suitable for students in Grades 8-10.

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