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The question asks for the formula of the nth term in the sequence: \(60, 150, 375, \dots\).

To determine this, let’s observe the ratio between consecutive terms:

\[
\frac{150}{60} = 2.5, \quad \frac{375}{150} = 2.5
\]

This indicates a geometric sequence with a common ratio \(r = 2.5\).

The general formula for the nth term of a geometric sequence is:

\[
a_n = a_1 \cdot r^{n-1}
\]

Where:
- \(a_1 = 60\) (the first term),
- \(r = \frac{5}{2}\) (common ratio).

Thus, the formula for the nth term is:

\[
a_n = 60 \cdot \left( \frac{5}{2} \right)^{n-1}
\]

From the given choices, the correct answer is:

\[
a_n = 60 \left( \frac{5}{2} \right)^{n-1}
\]

Do you have any questions or want further details?

### Related Questions:
1. How do you find the common ratio in a geometric sequence?
2. What is the difference between an arithmetic and a geometric sequence?
3. Can the nth term formula be applied to find any term in the sequence?
4. How would you determine the sum of the first n terms in this geometric sequence?
5. What happens if the common ratio is less than 1 in a geometric sequence?

### Tip:
Always check the common ratio in geometric sequences by dividing successive terms to verify if the pattern holds.

What is a formula for the nth term of the given sequence? 60, 150, 375...

Discover how to calculate the nth term of a geometric sequence where the first term is 60 and the common ratio is 2.5. Learn to apply the general nth term formula for geometric sequences. Suitable for Grades 9-12.

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