The problem asks for an expression to describe the sequence and to find the 9th term in the sequence.

The given sequence is: $-2, -4, -6, -8, \ldots$

Step 1: Identify the pattern

This is an arithmetic sequence, where the first term is $a_1 = -2$, and the common difference $d$ between consecutive terms is $-2$.

Step 2: General formula for the nth term of an arithmetic sequence

The formula for the nth term $a_n$ of an arithmetic sequence is: $a_n = a_1 + (n - 1) \cdot d$ Where:

• $a_1 = -2$ (the first term),
• $d = -2$ (the common difference),
• $n$ is the position of the term in the sequence.

Step 3: Expression for $a_n$

Substitute the values for $a_1$ and $d$ into the formula: $a_n = -2 + (n - 1) \cdot (-2)$ Simplifying: $a_n = -2 - 2(n - 1)$ $a_n = -2 - 2n + 2$ $a_n = -2n$ Thus, the expression for the nth term is: $a_n = -2n$

Step 4: Find the 9th term ($a_9$)

Substitute $n = 9$ into the expression: $a_9 = -2(9) = -18$

Final Answer:

• The expression for the nth term is $a_n = -2n$.
• The 9th term is $a_9 = -18$.

Would you like more details on any part of the explanation?

Here are some related questions to explore:

1. How would you find the sum of the first 9 terms in this sequence?
2. What is the difference between arithmetic and geometric sequences?
3. How would the formula change if the sequence had a positive common difference?
4. What happens to the formula if the sequence starts at a different first term?
5. Can you find the 20th term using the formula?

Tip: Always check the common difference in sequences to confirm if it’s arithmetic before applying the formula.