6. find the 8th term of the series 1/8, 1/4, 1/2 ..

The given series is:

\[
\frac{1}{8}, \frac{1}{4}, \frac{1}{2}, \dots
\]

This is a geometric sequence where the first term \( a_1 = \frac{1}{8} \), and the common ratio \( r \) can be found by dividing the second term by the first:

\[
r = \frac{\frac{1}{4}}{\frac{1}{8}} = 2
\]

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

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

To find the 8th term (\(a_8\)):

\[
a_8 = \frac{1}{8} \cdot 2^{8-1} = \frac{1}{8} \cdot 2^7 = \frac{1}{8} \cdot 128 = 16
\]

So, the 8th term of the series is:

\[
\boxed{16}
\]

Would you like further details on geometric sequences or have any questions?

Here are 5 related questions for practice:
1. What is the 10th term of the series \( 2, 4, 8, \dots \)?
2. How do you find the sum of the first \(n\) terms in a geometric series?
3. What is the common ratio in the sequence \( 3, 6, 12, \dots \)?
4. How do you determine if a sequence is geometric?
5. What is the 6th term of the sequence \( 5, 15, 45, \dots \)?

**Tip:** When working with geometric sequences, always double-check the common ratio before applying formulas.

6. Find the 8th term of the series 1/8, 1/4, 1/2 ..

Discover how to find the 8th term in the geometric sequence starting with 1/8, 1/4, 1/2 using the formula for the nth term of a geometric sequence. This solution breaks down the common ratio and the use of exponents, ideal for students in Grades 8-10.

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