To find the next number in the sequence \( 5, 7, 13, 31 \), let's analyze the pattern:

1. **First difference**:
   - \( 7 - 5 = 2 \)
   - \( 13 - 7 = 6 \)
   - \( 31 - 13 = 18 \)

   The first differences are \( 2, 6, 18 \).

2. **Second difference**:
   - \( 6 - 2 = 4 \)
   - \( 18 - 6 = 12 \)

   The second differences are \( 4, 12 \).

It appears that the second differences are increasing by a factor of 3. If we continue this pattern:

- The next second difference should be \( 12 \times 3 = 36 \).

Now, adding this to the last first difference:

- The next first difference should be \( 18 + 36 = 54 \).

Finally, add this to the last term in the sequence:

- The next term in the sequence should be \( 31 + 54 = 85 \).

So, the next number in the sequence is **85**.

Would you like further details, or do you have any questions?

Here are some related questions:
1. What are the common types of number sequences?
2. How do you find the nth term of a sequence?
3. What is the difference between arithmetic and geometric sequences?
4. How can you determine if a sequence is quadratic?
5. What are recursive sequences?
6. How do you identify patterns in complex sequences?
7. How do second differences relate to quadratic sequences?
8. What is the importance of recognizing patterns in sequences?

**Tip:** When analyzing sequences, always check the first and second differences to identify potential patterns, especially if the differences are consistent.

Learn how to find the next number in the sequence 5, 7, 13, 31 with a detailed step-by-step solution. This problem covers key concepts in number sequences and arithmetic progression. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation