To find the pattern in the series 3, 5, 13, 43, 177, ...?, observe the multiplicative and additive steps:
- 3 × 1 + 2 = 5
- 5 × 2 + 3 = 13
- 13 × 3 + 4 = 43
- 43 × 4 + 5 = 177
- 177 × 5 + 6 = 891
The pattern involves multiplying by consecutive integers and adding the next integer. Thus, the missing number is 891.
Therefore, the correct answer is (1) 891.