Type the next number in this sequence:

1,

2,

5,

10,

17,

26,

37,

To determine the next number in the sequence, let's analyze the pattern:

1. Find the differences between consecutive terms:  
   - \(2 - 1 = 1\)  
   - \(5 - 2 = 3\)  
   - \(10 - 5 = 5\)  
   - \(17 - 10 = 7\)  
   - \(26 - 17 = 9\)  
   - \(37 - 26 = 11\)  

2. The differences are: **1, 3, 5, 7, 9, 11**  
   - These differences form an arithmetic sequence with a common difference of **2**.

3. The next difference should be:  
   - \(11 + 2 = 13\)  

4. Add this to the last number in the sequence:  
   - \(37 + 13 = 50\)  

Thus, the next number in the sequence is **50**.

Would you like a deeper explanation or alternative methods?  

Here are five related questions for further exploration:  
1. What is the general formula for this sequence?  
2. How can you find the nth term of this sequence?  
3. What is an arithmetic sequence, and how does it relate to this pattern?  
4. Can you identify another sequence with similar properties?  
5. How would you use recursion to define this sequence?  

**Tip:** When analyzing number sequences, always check for common differences or ratios between terms first!

Type the next number in this sequence: 1, 2, 5, 10, 17, 26, 37

Learn how to determine the next number in the sequence 1, 2, 5, 10, 17, 26, 37. This problem explores arithmetic progressions and the method of finding differences between consecutive terms. Suitable for students in Grades 5-7.

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