Find the missing terms of the sequence. Then, determine if the sequence is arithmetic, geometric, or neither. Enter A for arithmetic, G for geometric, or N for neither.

5,9,13,17,⎯⎯⎯⎯⎯⎯,⎯⎯⎯⎯⎯⎯

To solve this, let's first identify the pattern in the sequence:

Given sequence: 5, 9, 13, 17, __, __

### Step 1: Find the pattern
To determine the pattern, we can subtract each term from the subsequent term:

- \(9 - 5 = 4\)
- \(13 - 9 = 4\)
- \(17 - 13 = 4\)

The difference between consecutive terms is constant at 4. This means the sequence is arithmetic.

### Step 2: Complete the sequence
Since the difference between terms is 4, we can find the next two terms by adding 4 to the last given term:

- \(17 + 4 = 21\)
- \(21 + 4 = 25\)

So, the complete sequence is: 5, 9, 13, 17, 21, 25.

### Step 3: Determine the type of sequence
Since the difference between consecutive terms is constant, the sequence is arithmetic.

**Final Answer:**
- Missing terms: 21, 25
- Type of sequence: A (Arithmetic)

Would you like more details or have any questions about this sequence? Here are some additional related questions:

1. What is the formula for the \(n\)th term of this arithmetic sequence?
2. How do you calculate the sum of the first \(n\) terms of an arithmetic sequence?
3. Can you determine the 10th term of this sequence?
4. What would happen if the difference between terms was negative?
5. How do you identify a geometric sequence?

**Tip:** In an arithmetic sequence, the difference between consecutive terms (called the common difference) is always the same.

Learn how to identify and complete an arithmetic sequence with the given terms 5, 9, 13, 17. Discover the formula for the nth term and the type of sequence. Suitable for Grades 7-9 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