Explanation:

Let’s dig into the series: 42, 42, 49, 75, 138, 269.

- Start by checking the differences:

- 42 to 42 = 0

- 42 to 49 = 7

- 49 to 75 = 26

- 75 to 138 = 63

- 138 to 269 = 131

- Look at those jumps. They don’t follow an obvious pattern. Maybe try ratios:

- 42/42 = 1

- 49/42 ˜ 1.17

- 75/49 ˜ 1.53

- 138/75 ˜ 1.84

- 269/138 ˜ 1.95

- Still not lining up. Let’s try squares or cubes—any pattern?

- 7, 26, 63, 131 — these are each one less than a cube:

- 7 = 2³ - 1

- 26 = 3³ - 1

- 63 = 4³ - 1

- 131 = 5³ - 1

- So the series builds like this:

- 1st term: 42

- 2nd term: 42 + (2³ - 1) = 42 + 7 = 49

- 3rd term: 49 + (3³ - 1) = 49 + 26 = 75

- 4th term: 75 + (4³ - 1) = 75 + 63 = 138

- 5th term: 138 + (5³ - 1) = 138 + 124 = 262 (not 269)

Here’s the thing: 269 is wrong, it should be 262.

So, here’s the breakdown:

- Option 1: 42 ? fits

- Option 2: 48 ? not in the series

- Option 3: 75 ? fits

- Option 4: 138 ? fits

- Option 5: 269 ? This is the incorrect one