To determine the next number in the sequence 6, 18, 20, 10, 30, 32, 16, we first need to analyze the pattern present in the numbers.
Let’s break it down:
- Starting with 6, it is followed by 18. This is an increase of 12.
- The next number, 20, is an increase of 2 from 18.
- Then we see a decrease to 10, which is a drop of 10.
- Next, there’s an increase to 30, up by 20.
- Following that, there’s a slight increase to 32, which adds 2.
- Finally, we see a decrease to 16, which is a drop of 16.
If we look closely at these changes, we can summarize the movements:
- +12, +2, -10, +20, +2, -16
From the pattern, it seems the sequence has alternating increases and decreases, with the increments and decrements varying. After a decrease to 16, we might expect another increase next.
Looking at the sequence, the last increment was a decrease of 16. If we analyze previous increases, we see a pattern where smaller increases of 2 often follow larger jumps. After 16, if we apply a reasonable increase of 20 (like the jump between 10 and 30), we arrive at:
16 + 20 = 36.
Therefore, based on this reasoning, the next number in the sequence should be 36.