Find the next four terms of the geometric sequence with = -6 and r= -2/3

The given geometric sequence has a first term \( a = -6 \) and a common ratio \( r = -\frac{2}{3} \).

To find the next four terms of the sequence, we will use the formula for the general term of a geometric sequence:

\[
a_n = a \cdot r^{n-1}
\]

However, we can also find each term by multiplying the previous term by the common ratio \( r \).

1. First term: \( a_1 = -6 \)
2. Second term: \( a_2 = -6 \cdot \left(-\frac{2}{3}\right) = 4 \)
3. Third term: \( a_3 = 4 \cdot \left(-\frac{2}{3}\right) = -\frac{8}{3} \)
4. Fourth term: \( a_4 = -\frac{8}{3} \cdot \left(-\frac{2}{3}\right) = \frac{16}{9} \)
5. Fifth term: \( a_5 = \frac{16}{9} \cdot \left(-\frac{2}{3}\right) = -\frac{32}{27} \)

Thus, the next four terms of the sequence are:

\[
4, -\frac{8}{3}, \frac{16}{9}, -\frac{32}{27}
\]

Would you like more details or have any further questions?

Here are 5 related questions for further practice:
1. What is the sum of the first 5 terms of the sequence?
2. What is the 10th term of this geometric sequence?
3. How would you find the nth term of this sequence?
4. What happens to the terms as \( n \) increases indefinitely?
5. How does the sequence change if \( r \) was a positive number?

**Tip:** In a geometric sequence, the common ratio \( r \) dictates how the sequence grows or decays. If \( |r| < 1 \), the terms get smaller over time.

Find the next four terms of the geometric sequence with a = -6 and r = -2/3.

Discover how to find the next four terms of a geometric sequence with first term a = -6 and common ratio r = -2/3. This detailed solution uses the general term formula for geometric sequences, showing step-by-step calculations. Ideal for students in Grades 9-11.

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