Explanation:

Let's break it down.

- The original set: (9, 26, 53)

- Look at the gaps: 26 - 9 = 17, 53 - 26 = 27 (not a simple sequence)

- Try other patterns:

- 9 × 2 + 8 = 26

- 26 × 2 + 1 = 53

- Not matching.

- How about adding squares?

- 9 + 3² = 18, but 26, so not matching

- What if it’s multiplying and adding:

- 9 × 3 - 1 = 26

- 26 × 2 + 1 = 53

- No easy arithmetic match.

- Let's now try another approach:

- Check “double plus something”: 9 × 2 = 18; 26 × 2 = 52.

- 26 - 9 = 17; 53 - 26 = 27.

- The jump is increasing by 10 (from 17 to 27).

- Try differences:

- 9 ? 26 (add 17)

- 26 ? 53 (add 27)

- Difference between additions: 27 - 17 = 10

- Apply that to the options:

Option 1: (5, 14, 29)

- 5 ? 14 (add 9)

- 14 ? 29 (add 15)

- 15 - 9 = 6 (Here, the gap is 6, not 10.)

Option 2: (6, 11, 36)

- 6 ? 11 (add 5)

- 11 ? 36 (add 25)

- 25 - 5 = 20 (Gap is 20.)

Option 3: (11, 32, 56)

- 11 ? 32 (add 21)

- 32 ? 56 (add 24)

- 24 - 21 = 3

Option 4: (7, 20, 42)

- 7 ? 20 (add 13)

- 20 ? 42 (add 22)

- 22 - 13 = 9

None is perfect. But let’s check: In the original, the differences (17?27) increased by 10. Now, for option 4, it's 13?22 = difference of 9. That’s the closest. Option 1's difference increments by 6; option 2 by 20; option 3 by 3.

So, if we're looking for the set where the increase between the first and second jump is closest to 10 (like in the original), option 4: (7, 20, 42) is the best match.

Option 4: (7, 20, 42) is correct.

Here’s the key:

- Check how the difference between the jumps grows.

- Only option 4 nearly matches the original pattern (increase close to 10).

- The other choices don’t come close.

Always check the increments of the increments—that's often the pattern in these series.