solve this exponential sequence 120,60,30,15

The sequence you provided is an exponential sequence:  
120, 60, 30, 15.

We can see that each term is half of the previous one:
- 120 → 60 (divide by 2)
- 60 → 30 (divide by 2)
- 30 → 15 (divide by 2)

Thus, this is a geometric sequence where the common ratio \( r = \frac{1}{2} \). The general formula for the nth term of a geometric sequence is:

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

Where:
- \( a_1 \) is the first term (120),
- \( r \) is the common ratio (1/2),
- \( n \) is the position of the term in the sequence.

### Formula:
\[
a_n = 120 \times \left(\frac{1}{2}\right)^{n-1}
\]

You can use this formula to calculate any term in the sequence.

Would you like further details on how to derive the formula or explore additional properties of this sequence?

Here are some related questions you might be interested in:
1. How can you find the sum of the first n terms of a geometric sequence?
2. What is the nth term in this sequence if n = 10?
3. How would the sequence change if the common ratio were 3 instead of 1/2?
4. Can the sum of an infinite geometric sequence exist for this sequence?
5. How does this sequence relate to exponential decay in real-world problems?

**Tip:** In a geometric sequence, if the common ratio's absolute value is less than 1, the sequence converges to zero as n increases.

Learn how to solve the geometric sequence 120, 60, 30, 15, where each term is half of the previous one. Understand the concept of geometric sequences, the common ratio, and use the formula a_n = 120 × (1/2)^(n-1) to find any term in the sequence. Suitable for students in Grades 8-10.

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