The first six terms in a geometric sequence are shown, where a1= -2 . -2, 4, -8, 16, -32, 64.... Based on this information, which equation can be used to find the nth term in the sequence, an?

To find the \( n \)th term of a geometric sequence, we use the formula:

\[
a_n = a_1 \cdot r^{n-1}
\]

where:
- \( a_1 \) is the first term of the sequence,
- \( r \) is the common ratio,
- \( n \) is the term number.

In this sequence:
- The first term, \( a_1 \), is \( -2 \).
- To find the common ratio \( r \), we divide the second term by the first term:

\[
r = \frac{4}{-2} = -2
\]

So, the common ratio \( r \) is \( -2 \). Now we can substitute \( a_1 = -2 \) and \( r = -2 \) into the formula for \( a_n \):

\[
a_n = -2 \cdot (-2)^{n-1}
\]

Therefore, the equation to find the \( n \)th term, \( a_n \), is:

\[
a_n = -2 \cdot (-2)^{n-1}
\]

Would you like further explanation or have any questions?

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1. How do you identify the common ratio in a geometric sequence?
2. Can the common ratio in a geometric sequence be negative?
3. What is the effect of a negative common ratio on the sequence terms?
4. How would the formula change if the first term were positive?
5. How can we determine if a sequence is geometric?

**Tip:** In a geometric sequence, the terms alternate in sign if the common ratio is negative.

The first six terms in a geometric sequence are shown, where a1= -2. -2, 4, -8, 16, -32, 64.... Based on this information, which equation can be used to find the nth term in the sequence, an?

Learn how to determine the equation for the nth term in a geometric sequence where the first term is -2, and each term has a common ratio of -2. Understand how to identify key sequence properties and use the formula an = a1 * r^(n-1) to find any term in the sequence. Suitable for students in Grades 9-10.

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