https://file.aiquickdraw.com/mathbot/file/1729802788695o3b59o4w.jpg

Let's solve the problem presented in the image.

1) **Create an equation for the geometric sequence:**
   The general formula for the \( n \)-th term of a geometric sequence is given by:
   \[
   a_n = a_1 \cdot r^{n-1}
   \]
   where:
   - \( a_1 \) is the first term,
   - \( r \) is the common ratio,
   - \( n \) is the term number.

   In this case:
   - \( a_1 = 5 \) (the first term),
   - \( r = 6 \) (the common ratio).

   Thus, the equation for the \( n \)-th term of the sequence is:
   \[
   a_n = 5 \cdot 6^{n-1}
   \]

2) **Find the 5th term of the sequence:**
   To find the 5th term, we plug \( n = 5 \) into the equation:
   \[
   a_5 = 5 \cdot 6^{5-1} = 5 \cdot 6^4
   \]
   Calculating \( 6^4 \):
   \[
   6^4 = 6 \times 6 \times 6 \times 6 = 1296
   \]
   Now, calculate \( a_5 \):
   \[
   a_5 = 5 \cdot 1296 = 6480
   \]

So, the 5th term of the sequence is **6480**.

Would you like more details, or do you have any questions?

Here are 5 related questions:
1. How do you derive the general formula for a geometric sequence?
2. What is the difference between geometric and arithmetic sequences?
3. How would the sequence change if the common ratio was negative?
4. How do you find the sum of the first \( n \) terms of a geometric sequence?
5. What happens to the terms in a geometric sequence when the common ratio is between 0 and 1?

**Tip:** The common ratio determines how quickly the terms of the geometric sequence grow (or shrink). A ratio greater than 1 leads to rapid growth, while a ratio between 0 and 1 results in decay.

The first term of a geometric sequence is 5 and the common ratio is 6. 1) Create an equation for the situation. 2) Find the 5th term of the sequence.

Learn how to solve a geometric sequence where the first term is 5 and the common ratio is 6. This step-by-step solution walks through creating the equation and finding the 5th term. Suitable for Grades 9-11.

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