Explanation:

Let’s analyze the sequence: 164, 172, 145, ?, 84

- First, look at the pattern between numbers.

- 164 ? 172 (difference: +8)

- 172 ? 145 (difference: -27)

- If we look at the next, let’s try similar pattern (maybe subtracting and adding with increasing numbers).

- 145 ? ? (let’s call it x)

- ? ? 84 (difference: x - 84)

Checking possible options:

- Try Option 1: 209

- 164 ? 172 (+8)

- 172 ? 145 (-27: 8 × -3.375, unrelated, but odd drop)

- 145 ? 209 (+64)

- 209 ? 84 (-125)

- Try Option 2: 308

- 145 ? 308 (+163), huge jump, odd pattern shared.

- Try Option 3: 283

- Jump is too large.

- Try Option 4: 234

- 145 ? 234 (+89), does not make the following jump fit.

- Checking for a pattern with differences: +8, -27, next is +64? Pattern seems like: +8, -27, +64, -125 (which fits our differences for option 1):

- 164 +8 = 172

- 172 -27 = 145

- 145 +64 = 209

- 209 -125 = 84

- This sequence alternates adding and subtracting perfect squares:

- +2²×2=8

- -3³=27

- +4²=16, but 64 is 8²; so actually: add 2², subtract 3³, add 8², subtract 5³

- The correct number is 209

Option:1, 209