To determine the next number in the series 1, 2, 8, 48, 384, let’s first examine the relationships between the numbers.
Starting with the given sequence:
- 1
- 2
- 8
- 48
- 384
Now, let’s look at how each number is related to its predecessor:
- From 1 to 2, we can see that 1 is multiplied by 2. (1 × 2 = 2)
- Next, from 2 to 8, we multiply 2 by 4. (2 × 4 = 8)
- Then from 8 to 48, we multiply 8 by 6. (8 × 6 = 48)
- Finally, from 48 to 384, we multiply 48 by 8. (48 × 8 = 384)
We can see a pattern in the multipliers: 2, 4, 6, and 8. These multipliers are increasing by 2 each time. Following this pattern, the next multiplier should be 10.
Thus, to find the next number in the series, we take the last number (384) and multiply it by 10:
384 × 10 = 3840
So, the next number in the series is 3840.