The sequence \(224, \_, \_, \_, \_, 7\) appears to be a geometric sequence where the terms between 224 and 7 need to be filled in.

In a geometric sequence, each term is obtained by multiplying the previous term by a common ratio \(r\). To find the common ratio and fill in the missing terms, we'll use the fact that the first term (\(a_1\)) is 224 and the sixth term (\(a_6\)) is 7.

The formula for the \(n\)th term of a geometric sequence is:

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

Given:
- \(a_1 = 224\)
- \(a_6 = 7\)

We can express \(a_6\) as:

\[
7 = 224 \times r^{5}
\]

Solving for \(r\), we get:

\[
r^5 = \frac{7}{224}
\]

Now let's solve for \(r\) and find the missing terms.

Learn how to solve the problem of filling in missing terms in a geometric sequence (224, __, __, __, __, 7). Understand the formula for the nth term of a geometric sequence and apply it to find the missing terms. Suitable for advanced high school students.

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