ANSWER IT AND GIVE THE SOLUTION Determine the next term 15 in the geometric sequence: 3,9,27,81

The given sequence is:

\[ 3, 9, 27, 81, \dots \]

This is a **geometric sequence**, where each term is obtained by multiplying the previous term by a constant factor (called the common ratio).

To find the common ratio \( r \), we divide any term by its preceding term:

\[
r = \frac{9}{3} = 3
\]

Since the common ratio \( r = 3 \), we multiply the last term (81) by 3 to find the next term.

\[
\text{Next term} = 81 \times 3 = 243
\]

### Solution:
The next term in the geometric sequence is **243**.

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Would you like further details on this? Here are five related questions to explore:

1. How do you find the nth term of a geometric sequence?
2. Can you calculate the sum of the first 10 terms of this sequence?
3. What if the common ratio is negative, how does that affect the sequence?
4. How would the sequence change if it started at a different number?
5. What is the significance of geometric sequences in real-life applications?

**Tip:** In a geometric sequence, the ratio between consecutive terms remains constant throughout!

Determine the next term 15 in the geometric sequence: 3,9,27,81

Discover how to find the next term in the geometric sequence 3, 9, 27, 81. Learn the step-by-step solution, including finding the common ratio and applying it to determine the following term. Suitable for students in Grades 6-8.

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