To solve this sequence problem, we analyze the given terms:

The sequence provided is: $15, 60, 240, 960$.

Step 1: Identify the Pattern

Each term in the sequence appears to grow by a factor of $4$:

• $60 = 15 \times 4$
• $240 = 60 \times 4$
• $960 = 240 \times 4$

This implies a geometric progression with:

• First term $a_1 = 15$
• Common ratio $r = 4$

Step 2: General Formula for a Geometric Sequence

The general form of a geometric sequence is: $a_n = a_1 \cdot r^{n-1}$ Substitute $a_1 = 15$ and $r = 4$: $a_n = 15 \cdot 4^{n-1}$

Step 3: Match with the Options

The correct formula from the options provided is: $a_n = 4^{n-1} \cdot 15$

Would you like further explanations or examples?

Here are five follow-up questions:

1. How do you determine the common ratio in a geometric sequence?
2. What is the explicit formula for a sequence if the first term and common ratio are different?
3. Can you calculate the 5th term of this sequence using the explicit formula?
4. How does this formula change if the sequence starts from $n = 0$?
5. What is the relationship between arithmetic and geometric sequences?

Tip: When identifying patterns in a sequence, check for constant differences (arithmetic) or constant ratios (geometric).