find the seventh term of the sequence negative 5, 15, negative 45

The sequence provided is: \(-5, 15, -45, \dots\).

To find the seventh term, we first need to determine the pattern or rule governing the sequence. This sequence appears to be a geometric sequence where each term is multiplied by a common ratio to obtain the next term.

### Step 1: Identify the common ratio
The common ratio \( r \) can be found by dividing the second term by the first term:
\[
r = \frac{15}{-5} = -3
\]
Thus, each term is multiplied by \(-3\) to get the next term.

### Step 2: Use the formula for the \(n\)th term of a geometric sequence
The formula for the \(n\)th term \(a_n\) of a geometric sequence is:
\[
a_n = a_1 \cdot r^{n-1}
\]
Where:
- \(a_1\) is the first term,
- \(r\) is the common ratio, and
- \(n\) is the term number.

### Step 3: Calculate the seventh term
For the seventh term (\(n = 7\)):
\[
a_7 = -5 \cdot (-3)^{7-1}
\]
\[
a_7 = -5 \cdot (-3)^6
\]

### Step 4: Evaluate the power
\[
(-3)^6 = 729
\]
\[
a_7 = -5 \cdot 729 = -3645
\]

So, the seventh term of the sequence is \(-3645\).

Would you like details on how I calculated this or have any questions?

Here are 5 questions related to the topic:
1. How do you determine if a sequence is arithmetic or geometric?
2. What is the formula for finding the sum of the first \(n\) terms in a geometric sequence?
3. Can a sequence have a common ratio of zero?
4. How do you solve for an unknown term in an arithmetic sequence?
5. What happens to a geometric sequence if the common ratio is a fraction?

**Tip:** Always check whether a sequence is arithmetic or geometric by examining the difference or ratio between consecutive terms.

Learn how to find the seventh term of a geometric sequence with a detailed step-by-step solution. This sequence -5, 15, -45 follows a specific pattern governed by the common ratio. Suitable for high school students studying geometric sequences.

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