https://file.aiquickdraw.com/mathbot/file/1727362691635hbc7rnvr.jpg

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.

Write an expression to describe the sequence below, and then find the 9th term. Use n to represent the position of a term in the sequence, where n = 1 for the first term. Sequence: -2, -4, -6, -8, ...

Learn how to find an expression for an arithmetic sequence and determine the 9th term in the sequence: -2, -4, -6, -8. This problem focuses on key algebraic concepts and the arithmetic sequence formula. Suitable for students in Grades 8-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation