Final answer:
The pattern in the series involves alternately multiplying by 3 and adding or subtracting 1. Continuing the pattern after 2, 5, 14, 41, and 122, we multiply 122 by 3 and add 1 to get the next number, which is 367.
Step-by-step explanation:
To determine which number comes next in the series 2, 5, 14, 41, 122, we need to identify the pattern. We observe that each number is being multiplied by a certain incrementing value:
- 2 to 5 is 2 × 2 + 1
- 5 to 14 is 5 × 3 - 1
- 14 to 41 is 14 × 3 + 1
- 41 to 122 is 41 × 3 - 1
We can see the pattern involves alternately multiplying by 3 and adding or subtracting 1. Continuing this pattern, we should multiply 122 by 3 and add 1, since we subtracted 1 in the last step.
122 × 3 + 1 = 366 + 1 = 367.
Therefore, the next number in the series is 367.