four arithmetic sequence between 24 and -2

To find four arithmetic means (numbers) between 24 and -2, we need to create an arithmetic sequence where the first term is 24, the fifth term is -2, and there are four terms between them.

An arithmetic sequence follows the rule:

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

Where:
- \(a_n\) is the \(n\)-th term,
- \(a_1\) is the first term,
- \(d\) is the common difference between consecutive terms,
- \(n\) is the term number.

Here, we know:
- \(a_1 = 24\),
- \(a_5 = -2\),
- \(n = 5\).

Using the formula for the fifth term:

\[
a_5 = a_1 + (5 - 1) \cdot d
\]
\[
-2 = 24 + 4d
\]
\[
-2 - 24 = 4d
\]
\[
-26 = 4d
\]
\[
d = \frac{-26}{4} = -6.5
\]

Now that we have \(d = -6.5\), we can find the four arithmetic means (terms between 24 and -2) by calculating each term:

- Second term: \(a_2 = a_1 + d = 24 - 6.5 = 17.5\),
- Third term: \(a_3 = a_1 + 2d = 24 - 2(6.5) = 11\),
- Fourth term: \(a_4 = a_1 + 3d = 24 - 3(6.5) = 4.5\).

Thus, the four arithmetic means between 24 and -2 are:

\[
17.5, 11, 4.5, -2
\]

Would you like any further details or explanations?

Here are five related questions to explore:
1. How do you calculate the common difference in an arithmetic sequence?
2. What happens when there are more than four terms between two numbers?
3. Can an arithmetic sequence contain only negative terms?
4. How do you solve for the \(n\)-th term of an arithmetic sequence?
5. What is the formula for the sum of an arithmetic sequence?

**Tip:** Always double-check your common difference when solving arithmetic sequences to avoid errors in intermediate terms.

Learn how to calculate four arithmetic means between 24 and -2 using the arithmetic sequence formula. This problem demonstrates how to determine the common difference and find intermediate terms in an arithmetic progression. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation