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

The given series is:

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

This is a geometric progression (GP) because each term is obtained by multiplying the previous term by a constant ratio. Let's identify the first term (\(a\)) and the common ratio (\(r\)):

- First term (\(a\)) = \( \frac{1}{8} \)
- Common ratio (\(r\)) = \( \frac{\frac{1}{4}}{\frac{1}{8}} = 2 \)

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

\[
T_n = a \cdot r^{n-1}
\]

We are looking for the 8th term (\(T_8\)):

\[
T_8 = \frac{1}{8} \cdot 2^{8-1} = \frac{1}{8} \cdot 2^7 = \frac{1}{8} \cdot 128 = \frac{128}{8} = 16
\]

Thus, the 8th term of the series is **16**.

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Here are 5 related questions for practice:
1. What is the 10th term of the same series?
2. What is the sum of the first 8 terms of this series?
3. Can you find the common ratio in a different way?
4. What would the first negative term be in this GP if extended?
5. How does the sum of infinite terms of a geometric series work?

**Tip:** In a geometric progression, knowing the first term and the common ratio allows you to calculate any term easily with the formula \( T_n = a \cdot r^{n-1} \).

Learn how to find the 8th term of the geometric progression series 1/8, 1/4, 1/2... using the GP nth term formula. This detailed solution explains the step-by-step process and the key concepts of sequences and progressions. Suitable for students in Grades 9-10.

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