16, 17, 13, 22, ?

Options

A. 15
B. 6
C. 12
D. 29

Explanation

To solve the series: 16, 17, 13, 22, ?, we will analyze the pattern step by step.

### Step-by-Step Solution:

1. **Identify the first two numbers:**
- The first number is 16 and the second number is 17.
- To go from 16 to 17, we add 1.
- **Calculation:** 16 + 1 = 17

**Hint:** Look for a simple arithmetic operation between the first two numbers.

2. **Identify the transition from the second to the third number:**
- The second number is 17 and the third number is 13.
- To go from 17 to 13, we subtract 4.
- **Calculation:** 17 - 4 = 13

**Hint:** Check if the operation is addition or subtraction and what the difference is.

3. **Identify the transition from the third to the fourth number:**
- The third number is 13 and the fourth number is 22.
- To go from 13 to 22, we add 9.
- **Calculation:** 13 + 9 = 22

**Hint:** Look for a pattern in the operations used so far.

4. **Establish the pattern:**
- The operations so far are:
- From 16 to 17: +1 (which is 1^2)
- From 17 to 13: -4 (which is -2^2)
- From 13 to 22: +9 (which is 3^2)
- The pattern appears to alternate between adding and subtracting squares of consecutive integers.

5. **Determine the next operation:**
- Following the established pattern, the next operation should be subtracting the square of 4.
- **Calculation:** 22 - 16 = 6

**Hint:** Continue the pattern of alternating addition and subtraction with the next integer's square.

6. **Conclusion:**
- The missing number in the series is 6.

### Final Answer:
The missing number is **6**.