Question

Match each geometric sequence with its explicit or recursive formulas.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.

Answer 1

It seems you are looking for help with matching geometric sequences to their explicit or recursive formulas. However, I currently do not have the specific sequences or formulas provided in your question.

In general, here’s how you can identify the correct formulas:

1. **Explicit Formula for a Geometric Sequence**: The explicit formula for the \(n\)-th term of a geometric sequence can be expressed as:
\[
a_n = a_1 \cdot r^{(n-1)}
\]
where \(a_1\) is the first term and \(r\) is the common ratio.

2. **Recursive Formula for a Geometric Sequence**: The recursive formula states that each term is based on the previous one:
\[
a_n = a_{n-1} \cdot r
\]
with the initial term specified, such as \(a_1 = \text{value}\).

If you can provide the geometric sequences and the corresponding formulas, I would be happy to help you match them accurately!