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.