What comes next?
2, 6, 14, 30, ?

The correct answer is 62.

To find the next number in the sequence 2, 6, 14, 30, ?, let us analyze the relationship between consecutive terms.

Method 1: Analyzing the differences between consecutive terms

First, let us calculate the difference between each adjacent pair of numbers:

6 - 2 = 4
14 - 6 = 8
30 - 14 = 16

Observe the pattern in the differences: 4, 8, 16. Each difference is double the previous difference.

Following this pattern, the next difference should be:

16 × 2 = 32

Now, add 32 to the last term (30) to find the missing number:

30 + 32 = 62

Method 2: Using the relationship between successive terms

Alternatively, each term can be obtained by multiplying the previous term by 2 and then adding 2:

(2 × 2) + 2 = 6
(6 × 2) + 2 = 14
(14 × 2) + 2 = 30

Applying the same rule to 30:

(30 × 2) + 2 = 60 + 2 = 62

Both methods consistently give the answer as 62.