What comes after 4, 13, 41, 126, 382, ?

Correct option is A

Given:

- The sequence is: 4, 13, 41, 126, 382, ?.
- We need to determine the next number in the sequence.

Formula Used:

1. The differences between consecutive terms are analyzed to determine a pattern.
2. Observing the second and third differences helps identify a possible polynomial relation or other logic.

Solution:

1. Calculate the differences between consecutive terms:
13 - 4 = 9, 41 - 13 = 28, 126 - 41 = 85, 382 - 126 = 256.

2. Calculate the second differences:

28 - 9 = 19, 85 - 28 = 57, 256 - 85 = 171.

3. Observe the pattern of differences. The second differences are tripling at each step. Predict the next difference:

769 = 256 + 513

4. Add this difference to the last term in the sequence:

382 + 769 = 1151