What is the 20th term of the arithmetic sequence -20, -29, -38, -47,...?


The given arithmetic sequence is: 

\[
-20, -29, -38, -47, \dots
\]

In an arithmetic sequence, the nth term can be found using the formula:

\[
a_n = a_1 + (n - 1) \cdot d
\]

Where:
- \(a_n\) is the nth term,
- \(a_1\) is the first term,
- \(d\) is the common difference between the terms, and
- \(n\) is the position of the term in the sequence.

### Step 1: Find the common difference
The common difference \(d\) is the difference between consecutive terms:
\[
d = -29 - (-20) = -29 + 20 = -9
\]

### Step 2: Use the formula to find the 20th term
Now, plug the values into the formula:

- \(a_1 = -20\),
- \(d = -9\), and
- \(n = 20\).

\[
a_{20} = -20 + (20 - 1) \cdot (-9)
\]
\[
a_{20} = -20 + 19 \cdot (-9)
\]
\[
a_{20} = -20 + (-171)
\]
\[
a_{20} = -191
\]

So, the 20th term of the sequence is \(-191\).

Would you like further details or have any questions?

### Related Questions:
1. How do you find the sum of the first 20 terms of this arithmetic sequence?
2. What is the formula for the sum of an arithmetic sequence?
3. How would you find the nth term if the common difference was positive?
4. How do arithmetic sequences differ from geometric sequences?
5. Can you derive the nth term of a sequence with a variable common difference?

**Tip:** In arithmetic sequences, the difference between consecutive terms remains constant, which makes predicting future terms straightforward using the formula.

What is the 20th term of the arithmetic sequence -20, -29, -38, -47,...?

Learn how to find the 20th term of the arithmetic sequence -20, -29, -38,... using the arithmetic sequence formula. This step-by-step solution covers key algebraic concepts and is suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation