What is the next number in the sequence: 3, 6, 4, 8, 6, 12, 10?

To find the next number in the sequence, let’s first identify the pattern. The sequence appears to alternate between two operations:

1. In the first part of the sequence, every second number doubles the previous number:
• 3 to 6 (doubled)
• 4 to 8 (doubled)
• 6 to 12 (doubled)
2. In the second part, we subtract 2 from the number before it:
• 6 – 2 = 4
• 8 – 2 = 6
• 12 – 2 = 10

Following this pattern, after the last number (10), we would double it like we did with 3, 4, and 6. So, if we apply the doubling operation to 10, we get:

10 x 2 = 20

Therefore, the next number in the sequence is 20.