The problem you uploaded shows a geometric sequence with missing terms. The sequence starts as follows:

$3, \_ , 6, \_ , 12, \_ , 24$

Let's find the missing terms.

In a geometric sequence, each term after the first is found by multiplying the previous term by a constant ratio $r$.

1. From 6 to 12, the ratio $r$ is:

$r = \frac{12}{6} = 2$

2. From 12 to 24, the ratio is:

$r = \frac{24}{12} = 2$

So, the common ratio $r = 2$.

Now, let's find the missing terms:

• The second term: The first term is 3, so the second term is $3 \times 2 = 6$.
• The fourth term: The third term is 6, so the fourth term is $6 \times 2 = 12$.
• The sixth term: The fifth term is 12, so the sixth term is $12 \times 2 = 24$.

Thus, the complete sequence is:

$3, 6, 6, 12, 12, 24$

Would you like any additional details on this solution?

5 Relative Questions:

1. What is a geometric sequence, and how does it differ from an arithmetic sequence?
2. How do you find the common ratio in a geometric sequence?
3. How can you find the general term for any geometric sequence?
4. Can the common ratio in a geometric sequence be a fraction?
5. What happens if the common ratio is negative in a geometric sequence?

Tip:

When dealing with sequences, always verify the common ratio or difference to ensure consistency across the sequence.