The problem you uploaded asks to determine the missing terms in a geometric sequence with given values of 12 and 36.

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

Given terms:

• The second term is 12.
• The third term is 36.

To find the common ratio $r$, we can divide the third term by the second term:

$r = \frac{36}{12} = 3$

Now that we know the ratio is 3, we can work backward and forward to find the missing terms.

1. To find the first term (before 12), divide 12 by the ratio $r = 3$:

$\text{First term} = \frac{12}{3} = 4$

2. To find the fourth term (after 36), multiply 36 by $r = 3$:

$\text{Fourth term} = 36 \times 3 = 108$

Final sequence:

• The sequence is: 4, 12, 36, 108.

Would you like further details or have any questions?

Follow-up questions:

1. What is the general formula for a geometric sequence?
2. How would the sequence change if the common ratio was 2 instead of 3?
3. Can you find the 5th term of the sequence?
4. How does an arithmetic sequence differ from a geometric sequence?
5. Can you express the nth term of this geometric sequence?

Tip:

Always check the common ratio by dividing successive terms when working with geometric sequences!