Explanation:

Let’s break this sequence down:

- The series is: 189, 532, 316, ?, 377.

Let’s look for a pattern. Try alternating patterns—maybe subtraction and addition.

First, check differences:

- 532 - 189 = 343

- 316 - 532 = -216

- ? - 316 = x

- 377 - ? = y

See those numbers: 343 = 7³, 216 = 6³.

Looks like the pattern is:

- Add 343, subtract 216, add 125, subtract 64, ...

- Cubes in descending order? 7³, 6³, 5³, 4³...

So,

- Step 1: 189 + 343 = 532 (? 7³)

- Step 2: 532 - 216 = 316 (? 6³)

- Step 3: 316 + 125 = 441 (? 5³)

- Step 4: 441 - 64 = 377 (? 4³)

Therefore:

- The missing number is 441.

- Option 3 is correct.

- 441 fits the pattern—addition of cubes in order (alternating add/subtract).