https://file.aiquickdraw.com/mathbot/file/1727015909760rgssipem.jpg

We are given the sequence:  
\[ 5, \ 5\sqrt{3}, \ 15, \ 15\sqrt{3} \]

To find the next term, let's analyze the pattern:

1. **First term (5) to second term (5√3)**:  
   The second term is obtained by multiplying the first term by \(\sqrt{3}\).  
   \( 5 \times \sqrt{3} = 5\sqrt{3} \).

2. **Second term (5√3) to third term (15)**:  
   The third term is obtained by multiplying the second term by \(\frac{3}{\sqrt{3}}\) (or 3), simplifying the expression:
   \[
   5\sqrt{3} \times \frac{3}{\sqrt{3}} = 5 \times 3 = 15.
   \]

3. **Third term (15) to fourth term (15√3)**:  
   The fourth term is again a multiplication by \(\sqrt{3}\):
   \[
   15 \times \sqrt{3} = 15\sqrt{3}.
   \]

Therefore, the next term is obtained by multiplying \(15\sqrt{3}\) by \(\frac{3}{\sqrt{3}}\):
\[
15\sqrt{3} \times \frac{3}{\sqrt{3}} = 15 \times 3 = 45.
\]

Thus, the next term in the sequence is **45**.

Would you like more details or have any questions?

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Here are some related questions to explore this topic further:

1. Can you describe the general form of this sequence?
2. What would be the 6th term in this sequence?
3. Is there a specific formula you can derive for the nth term?
4. How does multiplying by \(\sqrt{3}\) affect the terms in a sequence?
5. Can you create a similar sequence using a different base number instead of 5?

**Tip:** Understanding patterns in sequences often helps when solving more complex problems involving recurrence relations!

Here is a sequence: 5, 5√3, 15, 15√3. Work out the next term.

Learn how to find the next term in a sequence involving multiplication with radicals. The sequence starts with 5, 5√3, 15, 15√3. Discover the pattern and calculate the next term step-by-step.

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