To find the next number in the sequence 3, 6, 4, 8, 6, 12, 10, we first need to analyze the pattern of the sequence.
- Looking at the numbers, let’s break them down:
- 3 to 6: This is an increase of 3.
- 6 to 4: This is a decrease of 2.
- 4 to 8: This is an increase of 4.
- 8 to 6: This is a decrease of 2.
- 6 to 12: This is an increase of 6.
- 12 to 10: This is a decrease of 2.
This suggests a pattern: the sequence increases by an increasing amount and then decreases by 2.
Here’s the breakdown of the increases:
- First increase: 3
- Second increase: 4
- Third increase: 6
Following this pattern, the next increase could logically be 8 (continuing the trend of increasing by 2).
If we add this value to the last number in the sequence:
- 10 + 8 = 18
Given that the next number after 10 in the sequence, following the established pattern of increasing values and the consistent decrease, should be 18.
Therefore, the next number in the sequence is 18.