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.