To find the 7th term of a geometric sequence, we use the formula for the $n$th term of a geometric sequence:

$a_n = a_1 \cdot r^{n-1}$

where:

• $a_1$ is the first term,
• $r$ is the common ratio,
• $n$ is the term number.

From the sequence given (9, 3, 1, ...):

• The first term $a_1 = 9$,
• The common ratio $r = \frac{3}{9} = \frac{1}{3}$.

Now, using the formula to find the 7th term ($n = 7$):

$a_7 = 9 \cdot \left(\frac{1}{3}\right)^{7-1} = 9 \cdot \left(\frac{1}{3}\right)^6$

$a_7 = 9 \cdot \frac{1}{729} = \frac{9}{729} = \frac{1}{81}$

Thus, the 7th term of the geometric sequence is $\frac{1}{81}$.

Would you like further details or have any questions?

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Here are 5 related questions to explore further:

1. How do you find the sum of the first $n$ terms of a geometric sequence?
2. What happens if the common ratio is negative in a geometric sequence?
3. How do you determine if a sequence is arithmetic or geometric?
4. How do you find the general formula for any term in a geometric sequence?
5. What is the difference between finite and infinite geometric series?

Tip: Always double-check the common ratio before applying the geometric sequence formula.