Explanation:

Let’s analyze each pair:

- 5 : 7

The difference is +2.

- 22 : 466

22 × 21 + 4 = 462 + 4 = 466

- ? : 271

Looking for a number such that n × (n – 1) + 4 = 271

So, n × (n – 1) = 267

n^2 – n – 267 = 0

Solving: n = (1 + v(1 + 4 × 267)) / 2 = (1 + v1069) / 2

v1069 ˜ 32.72

(1 + 32.72) / 2 = 16.86 (not an integer)

Let’s check the options for ?:

- 22: 22 × 21 + 4 = 466 (already done)

- 24: 24 × 23 + 4 = 552 + 4 = 556 (not 271)

- 17: 17 × 16 + 4 = 272 + 4 = 276 (not 271)

- 18: 18 × 17 + 4 = 306 + 4 = 310 (not 271)

None matched.

But if we just check n × (n – 1) = 271 (ignore +4 adjustment):

- v271 ˜ 16.46, so try 17: 17 × 16 = 272 (very close, but 272 not 271)

- Try 13: 13 × 12 = 156

- Try 19: 19 × 18 = 342

None fit exactly.

So, the closest pair with a similar pattern (×, then +4) between 22:466, 24:556, 17:276, 18:310.

While 17 yields 276, which is nearest to 271, strictly none is perfect.

But as per options, option 3 (17) is closest to the intended pattern if we allow a small error.

Therefore:

- Correct Answer:

Option 3: 17