A sequence can be generated by using
gn = 2(gn-1), where g1 = __
1
3
and n is a
whole number greater than 1. What
are the first 5 terms of the sequence?

The given recursive sequence is defined by the formula:

\[
g_n = 2 \cdot g_{n-1}, \quad \text{where} \quad g_1 = \frac{1}{3}
\]

This means each term is twice the previous term, and the first term \( g_1 = \frac{1}{3} \).

### Let's calculate the first 5 terms:

1. \( g_1 = \frac{1}{3} \)
2. \( g_2 = 2 \cdot g_1 = 2 \cdot \frac{1}{3} = \frac{2}{3} \)
3. \( g_3 = 2 \cdot g_2 = 2 \cdot \frac{2}{3} = \frac{4}{3} \)
4. \( g_4 = 2 \cdot g_3 = 2 \cdot \frac{4}{3} = \frac{8}{3} \)
5. \( g_5 = 2 \cdot g_4 = 2 \cdot \frac{8}{3} = \frac{16}{3} \)

### Therefore, the first 5 terms of the sequence are:

\[
\frac{1}{3}, \frac{2}{3}, \frac{4}{3}, \frac{8}{3}, \frac{16}{3}
\]

Would you like further details on this sequence?

### 5 Related Questions:
1. How can we find the \( n \)-th term of the sequence without recursion?
2. What would the 6th and 7th terms be?
3. How does this sequence behave as \( n \) increases?
4. Can this type of recursive sequence be expressed as a geometric series?
5. What is the sum of the first 5 terms of this sequence?

### Tip:
In recursive sequences, recognizing patterns early can help simplify further calculations.

A sequence can be generated by using gn = 2(gn-1), where g1 = 1/3 and n is a whole number greater than 1. What are the first 5 terms of the sequence?

Learn how to calculate the first 5 terms of the recursive sequence defined by gn = 2 * gn-1 with g1 = 1/3. This solution explores recursive formulas and the behavior of sequences. Suitable for students in Grades 8-10.

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