The problem asks to find the 8th term of a given geometric sequence:

Sequence: $4, 12, 36, 108, \dots$

We are given:

• First term ($a$) = 4
• Common ratio ($r$) = $\frac{12}{4} = 3$
• Term number ($n$) = 8

In a geometric sequence, the general term ($a_n$) is calculated using the formula: $a_n = a \cdot r^{n-1}$ Substituting the given values: $a_8 = 4 \cdot 3^{8-1} = 4 \cdot 3^7$ Now, calculate $3^7$: $3^7 = 2187$ So: $a_8 = 4 \cdot 2187 = 8748$ Thus, the 8th term of the sequence is $8748$.

Would you like further details or explanations?

Here are 5 related questions to deepen your understanding:

1. How would you find the 5th term of this sequence?
2. What is the sum of the first 8 terms of this geometric sequence?
3. How can you determine if a sequence is arithmetic or geometric?
4. What happens if the common ratio is less than 1? How would that affect the terms?
5. How does the formula for the nth term of a geometric sequence compare to that of an arithmetic sequence?

Tip: Always verify the common ratio by dividing consecutive terms to ensure the sequence is geometric.