Explanation:

- The series given is: 17, 20, 60, 64, 256, 261, 1305, ?

- Observe the differences in the sequence:

- 20 - 17 = 3

- 60 - 20 = 40

- 64 - 60 = 4

- 256 - 64 = 192

- 261 - 256 = 5

- 1305 - 261 = 1044

- There's an alternating pattern:

- 3, 4, 5 are added.

- 40, 192, 1044 are multiples of increasing powers of 4.

- Following this pattern, after 1305, add 6.

- This indicates the next number is 1305 + 6 = 1311.

- The given options are:

- Option 1: 1346

- Option 2: 1361

- Option 3: 1284

- Option 4: 1311

- The correct answer is Option 4: 1311