Let's analyze the sequence: \(-1, 2, 7, 14, 23, \dots\)

### Step 1: Calculate the Differences
We'll start by calculating the differences between consecutive terms:

- \(2 - (-1) = 3\)
- \(7 - 2 = 5\)
- \(14 - 7 = 7\)
- \(23 - 14 = 9\)

The first differences are \(3, 5, 7, 9\).

### Step 2: Check the Pattern in Differences
The differences themselves are increasing by 2 each time.

### Step 3: Predict the Next Difference
Following the pattern, the next difference should be:

\[
9 + 2 = 11
\]

### Step 4: Calculate the Next Term
Add this difference to the last term:

\[
23 + 11 = 34
\]

### Final Answer:
The next term in the sequence is **34**.

Would you like more details or have any questions? Here are some related questions you might explore:

1. What is the second difference for this sequence?
2. How do you find a general formula for sequences with a quadratic pattern?
3. Can you identify another sequence where the difference between terms increases by a constant?
4. What is the role of polynomial functions in creating sequences?
5. How would you find the nth term for this sequence?
6. How do arithmetic sequences differ from this type of sequence?
7. What happens if the differences between terms form a geometric sequence?
8. How could this sequence be modeled using a quadratic equation?

**Tip:** Sequences with increasing differences often follow a quadratic pattern, so check the second difference if the first differences aren't constant.

Explore the sequence -1, 2, 7, 14, 23, ... and find the next term using detailed analysis. Understand the pattern of increasing differences and predict the next term with step-by-step calculations. Suitable for students in Grades 7-9 studying arithmetic sequences and pattern recognition.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation