Which of the following numbers will replace the question mark (?) in the given series:
7, 13, ?, 145, 721, 4321?

Question

Which of the following numbers will replace the question mark (?) in the given series:  
7, 13, ?, 145, 721, 4321?

Accepted Answer

Given: 7, 13, ?, 145, 721, 4321

Let's look for a multiplication/addition pattern:

#### Step-by-step pattern check:

1. **From 7 to 13:**  
   7 × 2 - 1 = 14 - 1 = 13

2. **From 13 to ?:**  
   Let's call the missing number x.  
   If the pattern is: previous × n ± k

3. **From ? to 145:**  
   Let's try option 4 (37):

- 13 × 3 - 2 = 39 - 2 = 37

Now check from 37 to 145:
   - 37 × 4 - 3 = 148 - 3 = 145

Next, from 145 to 721:
   - 145 × 5 - 4 = 725 - 4 = 721

Next, from 721 to 4321:
   - 721 × 6 - 5 = 4326 - 5 = 4321

So, the pattern is:
- Multiply by increasing numbers (2, 3, 4, 5, 6)
- Subtract increasing numbers (1, 2, 3, 4, 5)

#### Therefore,
The missing number is **37**.

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**Thus, the correct answer is:**
**4. 37**

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