These are the first five terms of an arithmetic sequence.

1, 5, 9, 13, 17, . . .

What is the value of the 10th term in the sequence?

Responses

To find the value of the 10th term in an arithmetic sequence, we can use the formula for the \(n\)th term of an arithmetic sequence:

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

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

Given:
- \(a_1 = 1\)
- \(d = 5 - 1 = 4\)
- \(n = 10\)

Substituting the values into the formula:

\[
a_{10} = 1 + (10-1) \cdot 4 = 1 + 9 \cdot 4 = 1 + 36 = 37
\]

So, the value of the 10th term is **37**.

Would you like further details or have any questions?

Here are five related questions:
1. How would you find the 20th term in this sequence?
2. What is the sum of the first 10 terms in the sequence?
3. How can you determine the common difference from a sequence?
4. What would be the value of the 50th term in this sequence?
5. How would the sequence change if the common difference were doubled?

**Tip:** Understanding the formula for the \(n\)th term of an arithmetic sequence is crucial for quickly finding any term in the sequence.

Learn how to find the 10th term in the arithmetic sequence 1, 5, 9, 13, 17, ... using the formula for the nth term of an arithmetic sequence. Understand the concepts of arithmetic sequences, common differences, and calculating specific terms in sequences. Suitable for Grades 7-9 mathematics students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation