Explanation:

Let’s break down the pattern in the series:

- 5, 13, 22, 34, 51, 75, 108, 152, ?

Let’s look at how the numbers change:

- 13 - 5 = 8

- 22 - 13 = 9

- 34 - 22 = 12

- 51 - 34 = 17

- 75 - 51 = 24

- 108 - 75 = 33

- 152 - 108 = 44

Now, check the differences between these differences:

- 8, 9, 12, 17, 24, 33, 44

The difference this time:

- 9 - 8 = 1

- 12 - 9 = 3

- 17 - 12 = 5

- 24 - 17 = 7

- 33 - 24 = 9

- 44 - 33 = 11

Notice the pattern—each difference increases by 2:

- 1, 3, 5, 7, 9, 11

So, the *next* difference should be 13 (following the pattern).

- Next difference = 44 + 13 = 57

- Next series number = 152 + 57 = 209

Here’s what that means for your options:

- Option 1: 230

- Option 2: 203

- Option 3: 209 ??

- Option 4: 290

The answer is Option 3—209.