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.