MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
Write a recursive formula for the geometric sequence.
\[
\begin{array}{l}
a_{n}=\left\{\frac{4}{7}, \frac{1}{14}, \frac{1}{112}, \frac{1}{896}, \ldots\right\} \\
a_{1}=
\end{array}
\]

Step 1 ：The given sequence is a geometric sequence. In a geometric sequence, each term after the first is found by multiplying the previous term by a fixed, non-zero number called the ratio. We can find the ratio by dividing any term in the sequence by the previous term.

Step 2 ：sequence = \(\left\{\frac{4}{7}, \frac{1}{14}, \frac{1}{112}, \frac{1}{896}, \ldots\right\}\)

Step 3 ：ratio = \(\frac{1}{14} \div \frac{4}{7} = 0.125\)

Step 4 ：The ratio of the geometric sequence is 0.125. Now, we can write the recursive formula for the geometric sequence. The recursive formula for a geometric sequence is of the form \(a_n = a_{n-1} \cdot r\), where \(r\) is the ratio.

Step 5 ：Final Answer: The recursive formula for the given geometric sequence is \(\boxed{a_n = a_{n-1} \cdot 0.125}\), where \(a_1 = \frac{4}{7}\).