Explanation:

Let's analyze the pattern:

- 9 : 109

- Here, 109 is formed by multiplying 9 by 12 and adding 1. (9 × 12 = 108, 108 + 1 = 109)

- 7 : 71

- 71 is formed by multiplying 7 by 10 and adding 1. (7 × 10 = 70, 70 + 1 = 71)

- 13 : ?

- Following the pattern: Multiply by 16 and add 1. (Since each multiplier increases by 2: 10, 12, next would be 14, 16...)

- Apply the pattern:

- 13 × 16 = 208

- 208 + 1 = 209

Options:

- Option 1: 238

- Option 2: 229

- Option 3: 218

- Option 4: 209

Therefore, the correct answer is:

- The correct pattern is: multiply each number by the increasing even number (10,12,14,16) and then add 1.

- 13 × 16 + 1 = 209

- Option 4 fits this perfectly.